By unit conversion, the area of rectangular field park is 619.59 m².
We need to know about unit conversion to solve this problem. The unit conversion can be used to convert a unit to another unit. It can be defined as
a = xb
where a is unit a, b is unit b and x is the constant of conversion.
From the question above, we know that
w = 58.5 ft
l = 114 ft
Convert the width and length to meter (1 ft = 0.3048 m)
w = 58.5 ft
w = 58.5 x 0.3048 m
w = 17.83 m
l = 114 ft
l = 114 x 0.3048 m
l = 34.75 m
Find the area
A = w x l
A = 17.83 x 34.75
A = 619.59 m²
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Place the following types of electromagnetic radiation in order of increasing wavelength. Ultraviolet light, gamma rays, microwaves.
in order of increasing wavelength gamma rays <UV light,<Microwaves
We need to describe the relationship for electromagnetic wave ordering that is provided by:
Light travels at a speed of c=*v. The wavelength and frequency of the waves are and, respectively.
Then, since we are aware that the gamma ray (1018 1/s) has the highest frequency of these radiations and the microwave (108 1/s) has the lowest, we may say:
The ultraviolet spectrum is placed between microwave and gamma radiation at frequencies of 1016 1/s.
We can arrange these radiations from short to long wavelengths in the following manner:
gamma rays <UV light,<Microwaves
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Why do people with high blood pressure sweat
Answer: People may not sweat excessively because of the hypertension or higher blood pressure than 120/80 mm Hg. They are not directly related. It is possible that they get exhausted quicker than others, or they have anxiety (nervousness) and hence they sweat more. Normally excessive sweating comes from excessive activity from thyroid or pituitary glands.
An object is dropped from a roof of a building of height h. during the last second of its descent, it drops a distance h/3. calculate the height of the building.
An object is dropped from a roof of a building of height h, the height of the building is 145.5 m.
CalculationIt is given that
[tex]y_{last}[/tex]= h/3
[tex]t_{last}[/tex]= 1s
g= 9.8 m[tex]s^{-2}[/tex]
In first stage,
t1= (t-1)s y1 = 2h/3
vi1 = 0
according to the kinematic equation,
y1= v1t1 + 1/2 g[tex]t1^{2}[/tex]
then substituting all the values, we have
2h/3 = 1/2(9.8)[tex](t-1)^{2}[/tex]
⇒ h = 7.35[tex](t-1)^{2}[/tex] → 1
Then the final velocity can be calculated by
vf1=[tex]vi^{2}[/tex]+ g(t - 1)
vf1= 9.8(t - 1)
In the second stage,
t2= 1s
y2= h/3
g=9.5 m[tex]s^{-2}[/tex]
vi2 = vf1 = 9.8(t - 1)
Acoording to kinematic equation,
y2 = vi2 t2 + 0.5g[tex]t1^{2}[/tex]
substituting the values,
h/3 = 9.8(t - 1) + 4.9
⇒ h= 29.4(t - 1) + 14.7 → 2
From equation 1 and 2, we get,
7.35[tex](t-1)^{2}[/tex] = 29.4(t - 1) + 14.7
if we assume (t-1) = R, we get
7.35[tex]R^{2}[/tex] - 29.4R - 14.7 =0
⇒R = 4.45
t = R+1 = 5.45s
substituting the value of t in equation 1, we have
h= 7.35[tex](4.45)^{2}[/tex] = 145.5m
Thus, the height of the building is 145.5m.
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What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce the intensity to 0.56 times the original intensity?
41.55° angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce the intensity to 0.56 times the original intensity.
Assume that Io is the initial intensity and that is the angle between the polarizer and the filter axis.
After filtering, light has a 0.56 Io light intensity.
According to Malus's law, the amount of plane-polarized light that enters the analyzer is directly inversely proportional to the square of the cosine of the angle between the polarizer's plane and its transmission axis.
By applying the Malus law,
[tex]I = I_{0} Cos^{2}[/tex]θ
[tex]0.56I_{0} = I_{0} Cos^{2}[/tex]θ
[tex]0.56= Cos^{2}[/tex]θ
θ = 41.55°
Therefore, 41.55° angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce the intensity to 0.56 times the original intensity.
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To calculate the components of the initial velocity (vvivvi), you have to identify the correct motion equations.
A golfer hits a golf ball that travels 60 m across the field and takes 3.2 seconds to reach the ground.
What is the horizontal component of initial velocity?
Horizontal component of initial velocity = Vx = Cosθ x 18.75m/s
An object that is given an initial velocity and then affected by gravity is referred to as a projectile. These effects determine the course that the object takes. The object's trajectory is what we refer to as. A projectile's trajectory is determined by velocity in two dimensions. The projectile's x and y components each represent its horizontal and vertical motion, respectively. Meters are the units used to indicate both horizontal and vertical distances (m). Meters per second (m/s) is the unit used to express the horizontal and vertical velocities.
A projectile is in freefall once it has started moving. Gravity's downward acceleration is the sole acceleration that is having an effect on it. The magnitude of the acceleration caused by gravity (on Earth) is
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The density of a particular kind of glass is 2.40 g/cm^3 what is the volume of a 34.82?
The volume occupied of a particular kind of glass with a density of 2.40 g/cm^3l and a mass of 34.82 g is: 14.508 cm^3
The density formula and the procedure we will use is:
d = m/v
Where:
v= volumed= densitym= massInformation about the problem:
d= 2.40 g/cm^3m = 34.82 gv = ?Applying the density formula and clearing the volume we get:
d = m/v
v = m/ d
v = 34.82 g/2.40 g/cm^3
v = 14.508 cm^3
What is density?It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.
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If a pitcher throws a baseball with a speed of 89.0 mph, then how long is the ball in flight (in seconds)?
The baseball with a speed of 89.0 mph, has 8.12 s in flight
The formulas for the downward vertical launch and the procedures we will use are:
t max= v₀ / gt(of)=2*t maxWhere:
v₀ = initial velocityg = gravityt max = time to reach maximum heightt(of) = time of flightInformation about the problem:
g = 9.8 m/s²v₀ = 89.0 mpht max = ?t(of)=?Converting the velocity from mph to m/s, we have:
89 mil/h * (1609,34 m / 1 mil) * (1h / 3600 s) = 39.786 m/s
Applying the maximum time formula for a downward vertical launch, we get:
t max= v₀ / g
t max= 39.786 m/s / 9.8 m/s²
t max = 4.06 s
Applying the time of flight formula, we get::
t(of) =2 * t max
t(of) =2 * 4.06 s
t(of) = 8.12 s
What is vertical launch?In physics vertical launch is the motion described by an object that has been launched vertically in which the acceleration is the earth's gravitational force.
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After 55 years, what mass (in g) remains of a 200.0 g sample of a radioactive isotope with a half-life of 10.0 years?
By the half-life of radioactive, the remaining mass of radioactive elements is 4.42 grams.
We need to know about the half-life of the radioactive elements to solve this problem. The radioactive element will decay over time and follow the equation
N = No(1/2)^(t/t'')
where N is the final quantity, No is the initial quantity, λ is the decaying constant, t is time and t'' is the half-life of a radioactive element.
From the question above, we know that
t'' = 10 years
No = 200 g
t = 55 years
Calculate the remaining mass
N = No(1/2)^(t/t'')
N = 200(1/2)^(55/10)
N = 4.42 grams
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During a hard sneeze, your eyes might shut for 0.40 s. if you are driving a car at 77 km/h during such a sneeze, how far does the car move during that time?
The car with a velocity of 77 km/h, during a hard sneeze of 0.40 s, moves 8.56 m
Applying the distance formula from the uniformly rectilinear motion (URM), we have:
x = v * t
Where:
x = distancet = timev = velocityInformation about the problem:
v = 77 km/h t = 0.40 sx=?Converting the velocity units from km/h to m/s, we get:
77 km/h * (1000 m/ 1 km) * (1 h/ 3600 s) = 21.389 m/s
Applying the distance formula we have that:
x = v * t
x= 21.389 m/s * 0.40 s
x = 8.56 m
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
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Suppose that a and b are two independent events for which p(a) = 0.31 and p(b) = 0.76. find each of the following:
a. p(a|b) =______
b. p(b|a) =______
c. p(a and b) =______
d. p(a or b) =_______
The independent events are given below for the outcome provided :
P (A|B) = 0.76
P(B|A) = 0.76
P(A and B ) = 0.2356
P(A or B) = 0.2356
Understanding probability :
If A and B are independent, then knowing A doesn't give you any additional information about B and vice versa. Mathematically, this relationship are often represented with the two equations P(A|B) = P(B) and P(B|A)=P(B), as long as A and B are independent. differently to state this is that, no matter B, P(A) doesn't change, or A doesn't depend on B.
To (randomly) throw the primary dart into circle A and the second dart into circle B, you've got to get lucky on two separate occasions.
Simplifying the formula :
When throwing the primary dart, your chance of throwing it randomly into circle A is P(A). When throwing the second dart, your chance of throwing it randomly into circle B is P(B). Because the 2 are independent, the multiplication rule, which is usually P(A and B) = P(A|B) * P(B) can be simplified to P(A and B) = P(A) * P(B).
To (randomly) throw darts into either circle, you get two tries, once with A and once with B.
It’s possible that both darts land during a circle. Therefore, the overall addition rule holds, so P(A or B) = P(A) + P(B) - P(A and B).
Given the formulas italicized, you'll plug in your values for P(A) and P(B) to find the other probabilities:
P(A) = 0.31
P(B) = 0.76
Solving :P(A|B) = P(B)
P (A|B) = 0.76
P(B|A)=P(B)
P(B|A) = 0.76
P(A and B) = P(A) * P(B)
P(A and B ) = 0.31 ×0.76
= 0.2356
P(A or B) = P(A) + P(B) - P(A and B)
= 0.31 + 0.76 - 0.45
= 0.65
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1. Add together two vectors: the first has a magnitude of 95 units and is directed east; the other has a magnitude of 45 units directed at 45°to the first.
The addition of the two vectors is 130.75 units.
The term "vector" is used colloquially to describe constituents of particular vector spaces or some quantities that cannot be described by a single integer.
The magnitude of a vector formula can be utilized to determine the length of a given vector. This amount is essentially the distance between the vector's beginning point and ending point.
The first vector has a magnitude of 95 units and is directed east and the magnitude of the second vector is 45 units directed 45° to the first vector.
Let the magnitude of the first vector be [tex]|\overrightarrow A|=95[/tex].
Let the magnitude of the second vector be [tex]|\overrightarrow B|=45[/tex].
And the angle between the two vectors θ = 45°
Then, the sum of the two vectors will be:
[tex]|\overrightarrow A + \overrightarrow B| = \sqrt{A^2+B^2+2ABcos(\theta)}[/tex]
[tex]|\overrightarrow A + \overrightarrow B| = \sqrt{95^2+45^2+2(95)(45)cos(45^{\circ})}[/tex]
[tex]|\overrightarrow A + \overrightarrow B| = \sqrt{9025+2025+8550\frac{1}{\sqrt{2} } }[/tex]
[tex]|\overrightarrow A + \overrightarrow B| = \sqrt{11050+6045.76}\\|\overrightarrow A + \overrightarrow B| = \sqrt{17095.76 }\\|\overrightarrow A + \overrightarrow B| = 130.75[/tex]
The sum of the two vectors is 130.75 units.
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When looking to carry out a decision, one of the most critical elements in successfully implementing a solution is:_______
When looking to carry out a decision, one of the most critical elements in successfully implementing a solution is Planning.
psychology is the study of mind and behavior through scientific methodhindsight bias is the tendency to think that we may have predicted something that has already happened that we probably would not have been able to thought.scientific method is the set of premise , rules, and procedures that scientists use to deal empirical research.behaviorism is based on the premise that it is not possible to objectively study the mind, and therefore that psychologists should limit their attention to the study of behavior itself
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100 POINTS
1. In 1991, four English teenagers built an electric car that could attain a speed of 30.0 m/s. Suppose it takes 1 s for this car to accelerate from 7 m/s to 25 m/s. What is the magnitude of the car's acceleration?
2. What is the change in position, displacement, if a person moves from rest to 30 m away to the west?
15 m west
60 m west
30 m
30 m west
3.What would be the final velocity at the end of this fall if the initial velocity is 0 m/s and the time allowed to fall is 3 seconds?
29.4 m/s
44.1 m/s
12.81 m/s
Samuel is riding his bicycle 1.2 m/s to the east. How far does he go after 15s?
1.25 m
19 m
18 m
1.8 m
A deer runs out in front of this car and cause the driver to have to come to a stop. If the driver has an average acceleration of -6 m/s2 , how long will it take for him to stop if the car is travelling 12 m/s?
2 s
.5 s
-.5 s
-2 s
The answers are attached in the file.
Hope this helps :)
The acceleration of the electric car if it takes 1 s for this car to accelerate from 7 m/s to 25 m/s is 18 m/s².
What is acceleration?The term "acceleration" refers to the rate and direction at which velocity varies over time. Acceleration is the change in direction or speed of an object or points moving ahead. The frequent change in direction causes motion on a circle to rise even when the speed remains constant.
For all other motions, these effects increase the acceleration. Since acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is a vector quantity as well.
Given:
The initial speed of the electric car, u = 7 m/s,
The final speed of the electric car, v = 25 m/s,
Time taken, t = 1 sec,
Calculate the acceleration as shown below,
Acceleration = Final speed - Initial speed / time
Acceleration = 25 - 7 / 1
Acceleration = 18 / 1
Acceleration = 18
Thus, the acceleration of the car is 18 m/s².
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Outer edge of a wheel of radius 0.650 m. the wheel rotates at a constant rate of 230 rev/min. what is the speed (in m/s) of the drop of glue?
Outer edge of a wheel of radius 0.650 m. the wheel rotates at a constant rate of 230 rev/min. The speed is 15.65 m/s.
The wheel is rotating at a rate of 230rev/min. Convert it into radians per seconds.
1 rev/min = 2πrad/60s
0.1047 rad/s
Now,
To calculate the angular velocity of the wheel rotating at a rate of 230rev/min.
ω=230rev/min × 0.1074 rad/s/rev/min
ω=24.081 rad/s
Now to find the speed
v=rω
where
r = 0.650
ω= 24.081 rad/s
Putting the values
v = 0.650× 24.081
v=15.65 m/s.
The speed is 15.65 m/s.
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Why is it jazardous ro look directly into the crucible when the magnesium first reacts with the oxygen?
Answer:it can blind you
Explanation:
when magnesium reacts with oxygen it creats a light bright enough to blind you
A bike starting from rest acquires a speed of 40m/s in 20 seconds. Then, the bike travels with this speed for 15 seconds. Find the : Acceleration Distance travelled during acceleration, ,total distance travelled
Explanation:
i hope you can understand my calligraphy :)
The acceleration of the bike is 2 m/s². The distance traveled during acceleration is 100 m. The total distance covered by bike is 700m.
What is the equation of motion?The equations of motion can be described as the relationship between the acceleration (a), velocity, time (t), and displacement of a moving object.
The equations of motions can be demonstrated as follows:
[tex]v = u + at\\S = ut +(1/2)at^2\\v^2-u^2= 2aS[/tex]
Given, the initial speed of the bike, u = 0
The final speed of the bike, v = 40 m/s
The time takes to get this speed, t = 20 s
v = u + at
40 = 0 + a(20)
a = 2 m/s²
The distance traveled during acceleration, v²- u²= 2aS
(20)² - (0) = 2 ×2 ×S
S = 100 m
The total distance covered by the bike:
For the next 15 seconds, Distance = v ×t = 40 × 15 = 600 m
The total distance covered by bike = 100 + 600 = 700 m
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An airplane accelerates at 5.0 m/s2 for 30.0 s. during this time, it covers a distance of 10.0 km. what are the initial and final velocities of the airplane?
The initial velocity of the airplane is 258.3 m/s and then final velocity of the airplane is 408.3 m/s.
DescriptionWhen gravity first exerts force on an object, its initial velocity defines how quickly the object moves.
The final velocity, on the other hand, is a vector number that gauges a moving body’s speed and direction after it has reached its maximum acceleration.
CalculationAccording to laws of motion,
x = Vi*t = 1/2 at^2
Substituting all the values we have,
10^4 = vi (30) + 0.5(5)(30)
Simplifying it,
Vi = 258.3 m/s
According to motion equations,
Vf = Vi + at
Substituting all the values,
Vf = 258.3 + (30)(5)
Vf = 408.3 m/s
So, we have Initial velocity = 258.3 m/s and final velocity = 408.3 m/s
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Can you please help me?
You just walked up the tallest mountain in the United States and are sitting down at the top. How much work are you doing?
A. lot
B. none
C. a little bit
Answer: lot
Explanation: because you just climbed a mountain
The graph in Figure 13 represents the motion of a car moving along a straight highway. Describe in words the car’s motion.
Answer:
increasing the speed o
Explanation:
direction change
The graph which shows the position of the object at a particular time is called a position-time graph. The position of the object is increasing with time.
What is a position time graph?The graph which shows the position of the object at a particular time is called a position time graph.
In the given graph, The position of the object in the 1st minute was 50 m, and the position of the object in the 3rd minute was between 50 to 100. The position of the object at the 5th minute was in the range of 100 to 150 m.
The position-time graph shows the velocity of the object. The slope of the object gives the location of the object.
There are two types of graphs such as straight line graphs and curve graphs. If the graph is curved it is showing the slope of the object keeps on changing.
Therefore, The graph which shows the position of the object at a particular time is called the position-time graph. The position of the object is increasing with time.
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In c 11, assuming mychar is a char variable and mystring is a string, what is the value of mychar after the following statement executes? mychar = mystring.front();
The value of mychar after the statement executes is the first character of mystring.
What is C++11?
The ISO/IEC 14882 standard for the C++ programming language is known as C++11. The previous C++ standard, C++03, was replaced by C++11, which was then followed by C++14. Although it was formerly known as C++0x since it was anticipated to be published before 2010, the name now adheres to the custom of designating language versions by the publication year of the specification.
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If you throw a baseball straight up, what is its acceleration at the highest point?
The smallest unit of matter that retain all of the physical properties of that type of matter is?
The smallest unit of matter that retain all of the physical properties is Atom.
What is atom?The smallest component of ordinary stuff that makes up a chemical element is an atom. Atoms that are neutral or ionised make up every solid, liquid, gas, and form of plasma. Atoms are very tiny, measuring approximately 100 picometers across.
A chemical element is uniquely defined by its atoms, which are tiny pieces of substance. An atom is made up of a core nucleus and one or more negatively charged electrons that orbit it. The positively charged, comparatively hefty protons and neutrons that make up the nucleus may be present.
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A car , mass = 2000 kg, is traveling on a highway at a velocity of 20 m/s when it ploughs into a number of sand bags. the sandbags stop the car in 4.0 m what is the force on the car?
The force on the car is 1×10^5 N.
The work-energy theorem states that when a force displaces a body, the change in kinetic energy of the body is measured. Conversely, when an opposing force is applied to a body, the kinetic energy of the body decreases by the same amount. It loses kinetic energy. The bodies' loss of kinetic energy is equivalent to the labor they put into resisting the opposing force.
mass of the car, m = 2000 kg
the velocity of car , v = 20 m/s
distance traveled, s = 4 m
let the force on the car be F
using work-energy theorem
[tex]F\times s\times cos(180) = 0.5 \times m \times ( 0 - v^2)[/tex]
[tex]F \times 4 \times(-1) = 0.5\times 2000 \times ( 0 - 20^2)[/tex]
solving for F
[tex]F = 1 \times 10^5 N[/tex]
the force on the car is [tex]1 \times 10^5 N.[/tex]
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You are given pure samples of ammonia, nh3(g), and nitrogen trifluoride, nf3(g). what prediction would you make concerning their standard molar entropies at 298 k?
The standard molar entropies at 298 K is
S°Ammonia < S°Nitrogen trifluoride.
How are standard entropies calculated?The entropy of a substance can be calculated by measuring the amount of heat required to raise the temperature by a given amount in a reversible process. S° is the entropy of one mole of a substance in its standard state at one atmosphere of pressure.The difference between the sum of the molar entropies of the products and the sum of the molar entropies of the reactants can be used to calculate the change in the standard molar entropy of a reaction.The entropy or degree of randomness of one mole of a sample under standard state conditions is defined as standard molar entropy. The standard molar entropy unit is joules per mole Kelvin (J/molK).
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A bus leaves Houston at 6am headed toward Austin at a constant speed of 54.3 miles/hr. If Austin is located 190 miles west of Houston, approximately when will the bus arrive in Austin?
resolved for the constant speed as the ratio of distance and time. We have B as the speed, the, as the distance at the at the time it is given that the bus leaves easter and other exactly six o'clock in the morning In Travis at a constant speed of 54.3 mph to Austin, which is located at a distance of 190 miles away. We want to find the arrival time. So first is that satisfying the time of travel to suffer the time from the given equation. And we have B equals distance divided by the speed. The distance is 190 miles and the speed is 54.3 mph. We get time here in terms of R. S. S 3.5, So it takes three hours and three hours and 30 minutes to travel, he said distance. So if it's if the bus departs at the at the time of six of clubs, So three hours and 30 minutes after that, it will arrive to Austin. So that means the arrival time will be nine 30 in the morning, So that's three hours and 20 minutes. Oh, after six o'clock. So I hope everything is clear.
The scientific method can easily be misinterpreted as ___________. question 1 options: a great "magical trick", or slide of hands, rather than factual an "auto mechanics" guide to science investigation a "cookbook" recipe with linear steps for performing scientific investigations
It can be misinterpreted as a "cookbook" recipe for performing scientific investigations.
What one word best describes the scientific method?Through testing and experimentation, the scientific method is established through an unbiased manner.
The fundamental steps in these findings are Making an observation, formulating a hypothesis, making a prediction, carrying out an experiment, and then evaluating the findings.
Can any question be answered using the scientific method?There are limitations to the scientific process. Only quantitative data from observable, quantifiable, and repeatable experiments can it provide objective answers to questions.
It cannot provide an objective response to queries based on personal convictions or preferences, such as whether there are ghosts or deities present or who makes the finest doughnut.
What questions cannot be solved by science?The presence of any supernatural being or God cannot be established or disproven by science. Sometimes, attempts to provide a hand using scientific concepts.
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Which theoretical perspective is consistent with the idea that the mass media represents the idea's of the ruling class and is used to oppress the poor and powerless?
Social conflict theoretical perspective is consistent with the idea that the mass media represents the idea's of the ruling class and is used to oppress the poor and powerless.
Conflict in society arises when people compete for control or authority. Social conflict occurs when two or more individuals disagree with one another in social interactions and each employs reciprocal social power to pursue opposing but stop the other from achieving their own goals. In contrast to role conflict, which involves only two sides, social conflict involves multiple parties, including groups, organizations, communities, and crowds.
Making incorrect assumptions when there is uncertainty might lead to social conflict. Consider the difference between making a negative assumption, such as that a late friend doesn't respect your time, and a positive assumption, such as that they have encountered an issue, like a late train.
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What mass of sucrose, c12h22o11 would be needed to obtain the same freezing point when dissolved in 200 g of water as 5.00 g of kcl?
45.90kg mass of sucrose, would be needed to obtain the same freezing point when dissolved in 200 g of water as 5.00 g of KCl.
We can obtain the freezing point of solution using:
Δ[tex]T_{f}[/tex] = i × [tex]K_{f}[/tex] × m
[tex]m = \frac{moles}{volume of solvent in kg}[/tex]
[tex]m = \frac{mass/molarmass}{0.2}[/tex]
[tex]m = \frac{5/74.55}{0.2}[/tex]
m = 0.3353moles/kg
Now, Δ[tex]T_{f}[/tex] = i × [tex]K_{f}[/tex] × m
Δ[tex]T_{f}[/tex] = 2 × (-1.86) × 0.3353
Δ[tex]T_{f}[/tex] = -1.2473°C
Now, for obtaining mass of sucrose , using the same formula of freezing point we get:
Δ[tex]T_{f}[/tex] = i × [tex]K_{f}[/tex] × m
-1.2473 = 1 × (-1.86) × [tex]\frac{mass/342.3}{0.2}[/tex]
-1.2473 = -1.86 × [tex]\frac{mass/342.3}{0.2}[/tex]
-1.2473 = -1.86 × [tex]\frac{mass}{68.46}[/tex]
mass = 45.90kg
Therefore, 45.90kg mass of sucrose, would be needed to obtain the same freezing point when dissolved in 200 g of water as 5.00 g of KCl.
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How far from the heavy end of a 68.0-cm long bat would its center of gravity be if its is at one-fourth of the length of the bat?
The heavy end of a 68.0-cm long bat would be at 17cm far from its center of gravity.
The location where an object's weight is equally distributed on all sides is known as its center of gravity. For all practical purposes, the behavior would be almost unchanged if you substitute a point mass for the body at the center of gravity. The stability of an object is intimately related to its center of gravity.
We can solve finding if the center of gravity is at one-fourth the bat's length if [tex]c_{g} = \frac{1}{4} L[/tex]
where L = length of bat
[tex]c_{g} =\frac{1}{4} (68.0)[/tex]
[tex]c_{g} = 17cm[/tex]
Therefore, the heavy end of a 68.0-cm long bat would be at 17cm far from its center of gravity.
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A place kicker kicks a football with a velocity of 20 m/s and at an angle of 53 degrees
a) How long is the ball in the air?
b) How far away does it land?
c) How high does it travel?
(a) For 3.26sec long is the football in the air
(b) The football will land 39.24m far away
(c) The football will travel 13.01m high.
The vectors in x and y direction for football are as follows:
[tex]v_{y} = v_{o} sin53[/tex]
[tex]v_{y} = 15.97m/s[/tex]
[tex]v_{x} = v_{o} cos53[/tex]
[tex]v_{x} = 12.04m/s[/tex]
(a) According to equation of motion :
[tex]y = v_{y} t+\frac{1}{2} gt^{2}[/tex]
[tex]0 = (15.97)t+4.9t^{2}[/tex]
15.97 = 4.9t
t = 3.26seconds
Therefore, for 3.26sec long is the football in the air.
(b) Again using equation of motion:
[tex]x = v_{x} t[/tex]
x = 12.04 × 3.26
x = 39.24meters
Therefore, the football will land 39.24m far away.
(c) Dividing the time obtained in part (a) we get t = 1.63s
So, by using motion law we get,
[tex]y = v_{y} t+\frac{1}{2} gt^{2}[/tex]
[tex]y = (15.97)(1.63)+(4.9)(1.63)^{2}[/tex]
y = 13.01meters.
Therefore, the football will travel 13.01m high.
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