Answer:
a. t [tex]\simeq[/tex] 14.98 sec
b. x = 501.27 m
Explanation:
From the given information:
[tex]\dfrac{dv}{dt}=9.8-(\dfrac{v}{5 })[/tex] and [tex]v(0)=0[/tex]
[tex]\dfrac{dv}{dt}=\dfrac{49-v}{5 }[/tex]
[tex]\dfrac{dv}{49-v}=\dfrac{dt}{5 }[/tex]
Taking Integral of both sides
[tex]- ln(49-v) = \dfrac{t}{5} + C[/tex]
at t=0 we have v=0
This implies that
[tex]- ln(49-0) = \dfrac{0}{5} + C[/tex]
[tex]C= - ln(49)[/tex]
Thus:
[tex]\dfrac{t}{5} - In (49) = - In (49 -v) \\ \\ In(49) - \dfrac{t}{5} = In (49-v)[/tex]
[tex]49-v = e^{(-\frac{t}{5} +ln(49))}\\ \\ v = 49 - 49e^{(-\dfrac{t}{5})}[/tex]
The limiting velocity when the time is infinite is :
95% of 49 = 46.55
∴
[tex]0.05= e^{(-\dfrac{t}{5})}[/tex]
[tex]\dfrac{t}{5}= In(\dfrac{1}{0.05})[/tex]
[tex]\dfrac{t}{5}=2.9957[/tex]
t = 5 × 2.9957
t [tex]\simeq[/tex] 14.98 sec
b.) [tex]v = 49 - 49e^{(-\dfrac{t}{5})}[/tex]
[tex]v = \dfrac{dx}{dt}=49 - 49e^{(-\dfrac{t}{5})}[/tex]
[tex]dx=(49 - 49e^{(-\frac{t}{5})}) \ dt[/tex]
Taking integral of both sides.
[tex]x = 49t + 245 e^{(\frac{-t}{5})} +C[/tex]
at time t = 0 , distance x traveled = 0
∴
C= - 245
Therefore
[tex]x = 49t + 245 e^{(\frac{-t}{5})} -245[/tex]
replacing the value of t = 14.98
[tex]x = 49(14.98) + 245 e^{(\frac{-14.98}{5})} -245[/tex]
x = 501.27 m
A boy on a roof throws one ball downward and an identical ball upward. The ball thrown downward hits the ground with 100 J of kinetic energy. If both balls are thrown at the same speed and there is no air friction, what is the kinetic energy of the second just before it hits the ground
Answer:
It will be Less than 100J
Explanation:
Because the second ball has both kinetic and potential energy so just before it hits the ground the kinetic energy will be total energy-potential energywhich will be less than 100J
A nonconducting sphere of mass 18.5 kg and diameter 25.0 cm has 8.10 × 1015 electrons removed from it. The points of removal are spread uniformly throughout the volume of this sphere. A tiny neutral plastic ball of mass 0.120 g is placed just outside the surface of the large sphere and is then released. How many electrons must be removed from the plastic ball so that its initial acceleration just after being released will be 1525 m/s2? You can neglect gravity.
Answer:
The value is [tex]n = 1.527 *10^{14} \ electrons [/tex]
Explanation:
From the question we are told that
The mass of the sphere is m = 18.5 kg
The diameter is [tex]d= 25.0 \ cm = 0.25 \ m[/tex]
The number of electrons is [tex]N = 8.10 *10^{15} \ electrons[/tex]
The mass of the plastic ball is [tex]m_b = 0.120 g[/tex]
The initial acceleration of the ball is [tex]u = 1525\ m/s^2[/tex]
Generally the radius of the sphere is mathematically evaluated as
[tex]r = \frac{d}{2}[/tex]
=> [tex]r = \frac{0.25}{2}[/tex]
=> [tex]r = 0.125 \ m [/tex]
Generally the force between the ball and the sphere is
[tex]F = \frac{k * q_1 * q_2 }{r^2}[/tex]
Generally this force can also be mathematically represented as
[tex]F = m_b * a[/tex]
So
[tex] m_b * a = \frac{k * q_1 * q_2 }{r^2}[/tex]
Here [tex]q_1[/tex] is the charge removed from the sphere whicn is evaluated as
[tex]q_1 = N * e[/tex]
substituting [tex]1.60*10^{-19} \ C[/tex] for e
[tex]q_1 = 8.10 *10^{15} * 1.60*10^{-19}[/tex]
[tex]q_1 = 0.0013 \ C [/tex]
and [tex]q_2[/tex] is the charge to be removed from the ball
So
[tex] 0.120 * 1525 = \frac{9*10^9 * 0.0013* q_2 }{0.125^2}[/tex]
[tex]q_2 = 2.44 *10^{-7} \ C [/tex]
Generally the number of electron to be removed from the ball is mathematically represented as
[tex]n = \frac{q_2}{e}[/tex]
=> [tex]n = \frac{ 2.44 *10^{-7}}{1.60*10^{-19}}[/tex]
=> [tex]n = 1.527 *10^{14} \ electrons [/tex]
EXPLAINING ISSUES How did Rome’s status as a site of encounter change the lives of Roman citizen
Answer:
Below, the definition including its position of Roman people is clarified.
Explanation:
Conflicts began to rise in most of the other societies surrounding Rome, as Rome gained property mostly in the peninsula. They were requesting an improvement or change in one's position from these recently subjugated people. Though without the election, they might intermarry among Romans, negotiate agreements and also have freedom of movement brooking sine suffrage as well as citizenship, individuals also requested more.Any two objects that have mass will also have which type of force between them?
(5 points) +Brainiest
a
Magnetic
b
Gravitational
c
Nuclear
d
Chemical
Answer:
I think the answer for this question is number b. gravitational
Which statement is TRUE?
A) Energy can be created or destroyed.
B) Electrical energy is created from other forms of energy.
C) Energy in a battery makes new energy called electrical energy.
D) Stored energy in a battery can be transformed into electrical energy.
A 30-microfarad capacitor is charged to 90 v and then connected across an initially un charged capacitor of unknown capacitanc c .if the final potintial difference across the 30- microfarad capacitor is 20 v sitemin c
Answer:
The value is [tex] C_u = 5 *10^{-6} F[/tex]
Explanation:
From the question we are told that
The voltage of the capacitor is [tex]V = 90 \ V[/tex]
The capacitance of the capacitor is [tex]C = 30 \ \mu F = 30 *10^{-6} \ F[/tex]
The final voltage is [tex]V_a = 20 \ V[/tex]
Since the capacitors are connected in parallel we have that
[tex]Q_u = Q'_u + Q[/tex]
Where [tex]Q_u[/tex] is the charge of the known capacitor before it is connected to the known capacitor
[tex]Q_u' [/tex] is the charge of the known capacitor after it is connected
[tex]Q [/tex] is the charge of the unknown capacitor
Also the potential across the two capacitors will be the same (except for a loss due heat (it been converted to heat ))
So
[tex]CV = CV_a + C_u * V_a[/tex]
=> [tex] C_u * V_a = CV - CV_a [/tex]
=> [tex] C_u = \frac{CV - CV_a }{ V_a } [/tex]
=> [tex] C_u = \frac{ [30*10^{-6} *90] - [30*10^{-6} * 20] }{ 20 } [/tex]
=> [tex] C_u = 5 *10^{-6} F[/tex]
difference between boiling point and freezing point
Impulse is the______of the force and time of contact
Answer:
Product
Explanation:
Impulse is defined as the average force acting on an object times the time the force acts:
Impulse = F · Δt
A 200g mass is attached to a spring, of spring constant, k. The spring is compressed, 15cm from its equilibrium value. When released, the mass reaches a speed of 5m/s. What is the spring constant (in N/m)?
Answer:
The spring constant is 222.2 N/m
Explanation:
Given;
mass of the spring, m = 200 g = 0.2 kg
extension of the spring, x = 15 cm = 0.15 m
speed of the mass, v = 5 m/s
spring constant, k = ?
Apply law of conservation of energy;
¹/₂kx² = ¹/₂mv²
k = mv² / x²
k = (0.2 x 5²) / (0.15²)
k = 222.2 N/m
Therefore, the spring constant is 222.2 N/m
A tow truck is using a cable to pull the classic car up a 15o hill. If the classic car weighs 4000 lbs and the cable has a diameter of 3/4 inch, find the stress in the cable when the truck comes to a stop while on the hill. Ignore friction between the car and the pavement
Answer:
the stress in the cable at the time when the truck is stop is 2,344.57 lb/m^2
Explanation:
The computation of the stress in the cable when the truck comes to a stop is shown below:
We used the following formula
[tex]T = mg\times sin\theta\\\\= 4,000 \times sin15^{\circ}[/tex]
= 1,035.28
Now the stress in the cable is
Before calculating it first determined the area which is
[tex]Area = \frac{\pi}{4}\times (\frac{3}{4})^2 \\\\= \frac{9\pi}{64}[/tex]
So, the stress is
[tex]= \frac{T}{area}\\\\ = \frac{1,035.28}{\frac{9\pi}{64} }[/tex]
= 2,344.57 lb/m^2
Hence, the stress in the cable at the time when the truck is stop is 2,344.57 lb/m^2
What trend does the reactivity of nonmetals show in a periodic table? random changes without any trends on the periodic table changes according to trends on the periodic table increases from left to right across the periodic table decreases from left to right across the periodic table
Answer:
C) increases from left to right across the periodic table
Explanation:
if you're reading this, you better smile cause you aren't the only one stressed out about school :))) have a great day love
The trend of the reactivity of non metals in the periodic table is that it increases from left to right across the periodic table.
The periodic table is composed of metals on the left hand side and nonmetals on the right hand side.
As such, nonmetallic property increases from left to right across a period and so does the reactivity of nonmetals.
This implies that as we move from left to right across a period, nonmetallic elements become more reactive.
Learn more: https://brainly.com/question/23040395
which of the following temparature is approximately equal to room temperature
A)0k
B)o°c
C)293k
D)100°c
E)100k
Hello there! :)
[tex]\huge\boxed{\text{C. 293K}}[/tex]
Room temperature is approximately 20°C.
We can automatically eliminate choices B and D since they are not equal to 20°C.
Since some choices use the Kelvin scale, we can convert from Celsius to Kelvin using a simple formula:
K = C° + 273
Find room temperature in degrees Kelvin:
K = 20° + 273
K = 293°
Thus, the correct choice would be C. 293K.
A massive block is being pulled along a horizontal frictionless surface by a constant horizontal force. The block must be __________. View Available Hint(s) A massive block is being pulled along a horizontal frictionless surface by a constant horizontal force. The block must be __________. continuously changing direction moving at constant velocity moving with a constant nonzero acceleration moving with continuously increasing acceleration
Answer:
The body must be moving with a constant non zero acceleration.
Explanation:
Force produces acceleration on any mass it is applied on. The acceleration produced depends on the magnitude and direction of the force. For this block being dragged by a constant horizontal force, The body will undergo a constant non-zero acceleration that will steadily increase its velocity along the direction of the force.
A car is traveling 16 m/s East. If the car then speeds up at a constant acceleration, what is the direction of the car’s acceleration?
7.9x10^9 km is equal to?
Explanation:
7.9x10^9 km is equal to
=7900000000km
Please mark it as brainliast
The 45-g Wood Thrush migrates every spring from Central America to the United States to breed. The bird leaves its winter
home in Belize and travels 1422 km across the Gulf of Mexico to Louisiana. It then flies an additional 1343 km to reach
Virginia, where it spends the summer. The trip takes approximately 171 hours, flying mostly at night.
What is the average speed of the Wood Thrush?
Answer:
v = 16.16 km/h
Explanation:
Distance covered by Wood Thrush is 1422 km across the Gulf of Mexico to Louisiana + 1343 km to reach Virginia, where it spends the summer.
d = 1422 km + 1343 km
d = 2765 km
The trip takes approximately 171 hours, flying mostly at night, t = 171 hours
We need to find the average speed of the Wood Thrush. It can be given by :
[tex]v=\dfrac{d}{t}\\\\v=\dfrac{2765\ km}{171\ h}\\\\v=16.16\ km/h[/tex]
So, the average speed of the Wood Thrush is 16.16 km/h.
Calculate the potential difference of a wire of 10 ohm , through which 5 A of current is flowing .
2 V
50 V
0.2 V
0.5 V
What is the field outside the capacitor plates in a parallel capacitor?
Answer:
Zero
Explanation:
If using an ideal parallel plate capacitor, the electric field outside should be nearly zero.
During a relay race, runner A runs a certain distance due north and then hands off the baton to runner B, who runs for the same distance in a direction south of east. The two displacement vectors A and B can be added together to give a resultant vector R. Which drawing correctly shows the resultant vector?
Answer:
d) 4
Explanation:
The image attached shows the options.
The resultant vector is the resultant of two or more vectors. The resultant vector is gotten by adding the sum of the displacement of the vectors together (that is the sum of all the individual vectors).
From the question, since runner A runs north and runner B runs east the resultant vector would be the sum of the displacement of vectors A and B. Also, the direction of the vector would be the north east starting from the beginning of vector A to end of vector B. The correct option is d) 4
A jetliner, traveling northward, is landing with a speed of 71.9 m/s. Once the jet touches down, it has 675 m of runway in which to reduce its speed to 11.3 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing (take the direction of the plane's motion as positive).
Answer:
The value is [tex]a = -3.7 \ m/s^2 [/tex]
Explanation:
From the question we are told that
The landing speed is [tex]u = 71.9 \ m/s[/tex]
The distance traveled is [tex]d = 675 \ m[/tex]
The velocity it is reduced to is [tex]v = 11.3 \ m/s[/tex]
Generally the average acceleration is mathematically represented as
[tex]a = \frac{ v^2 - u^2 }{ 2 * d }[/tex]
=> [tex]a = \frac{ 11.3^2 - 71.9^2 }{ 2 * 675 }[/tex]
=> [tex]a = -3.7 \ m/s^2 [/tex]
g Two tiny identical spheres of mass m = 66.7 g carry identical positive charge q. The charges hang from identical massless threads of length L = 84.8 cm attached to a ceiling at the same point. The spheres repel, and the angle between the threads is θ = 33o. Find q, the charge on each sphere, in μC.
Answer:
Explanation:
a
The angle each thread is making with the vertex = 16.5 degree
weight acting downwards = 66.7 x 10⁻³ x 9.8 N .
distance between two charges = 2 x 84.8 x 10⁻² sin 33/2
= .48 m
repulsive force between the two charges
= 9 x 10⁹ x q² / .48²
F = 39 x 10⁹ q²
Now, the tension in the thread be T
T cos 16.5 = mg
T sin 16.5 = F
dividing
tan 16.5 = F / mg = 39 x 10⁹ x q² / 66.7 x 10⁻³ x 9.8
.296 x 66.7 x 10⁻³ x 9.8 = 39 x 10⁹ x q²
q² = 4.96 x 10⁻¹²
q = 2.23 x 10⁻⁶ C
= 2.23 μC
A hot air balloon is descending with a velocity of 2.0 m/s straight down. At a height of 6m, a champagne bottle is opened to celebrate a successful flight, expelling the cork horizontally with a velocity of 5.0 m/s. a. What is the initial velocity (magnitude and direction) of the cork, as seen by an observer on the ground? b. What are the horizontal and vertical components of the initial velocity? c. How long is the cork in the air? d. How far away from the balloon does it land?
Answer:
a
[tex]v = 5.39 \ m/s[/tex]
b
Horizontal component
[tex]v_x = 5.00 \ m/s[/tex]
vertical component
[tex]v_y = - 2.0 \ m/s[/tex]
c
[tex]t = 0.921 \ s[/tex]
d
[tex]d = 4.605 \ m [/tex]
Explanation:
Generally from the question we can deduce that he initial velocity of the cork, as seen by an observer on the ground in terms of the x unit vector is
[tex]v_x = 5.00 \ m/s[/tex] due to the fact that the cork is moving horizontally
Generally from the question we can deduce that the vertical and horizontal components of the initial velocity is
[tex]v_y = - 2.0 \ m/s[/tex] due to the fact that the balloon is moving downward which is the negative which will also cause the cork to move vertically with the balloon speed
Generally the initial velocity (magnitude and direction) of the cork, as seen by an observer on the ground is mathematically represented as
[tex]v = \sqrt{ v^2 _x + v^2 _y }[/tex]
[tex]v = \sqrt{ 5^2 + (-2)^2 _y }[/tex]
[tex]v = 5.39 \ m/s[/tex]
Generally the initial direction of motion as seen by the same observer is mathematically represented as
[tex]\theta = tan^{-1}[\frac{2}{5} ][/tex]
[tex]\theta = 21.80^o[/tex]
Generally the time taken by the cork in the air before landing is mathematically represented as
[tex]D = ut + \frac{1}{2} g t^2[/tex]
So D = 6 \ m from the question
g = 9.8 \ m/s^2
u = [tex]v_y[/tex] = 2 m/s this because we are considering the vertical motion
So
[tex]6 = 2 t + \frac{1}{2} * 9.8* t^2[/tex]
[tex]6 = 2 t + 4.9 t^2[/tex]
Solving using quadratic formula w have that
[tex]t = 0.921 \ s[/tex]
Generally the distance of the cork from the balloon is mathematically represented as
[tex]d = v_x * t[/tex]
[tex]d = 5 * 0.921 [/tex]
[tex]d = 4.605 \ m [/tex]
Children are told to avoid standing too close to a rapidly moving train because they might get sucked under it. Is this possible? Explain.
Answer:
no its not like the undertow in the ocean
Explanation:
Answer:
Yes
Explanation:
This is possible due to Bernoulli's principle.
A car starts 20 miles north of town then travel for 40 minutes until it is 100 miles north of town. What is the cars velocity over this time frame?
a supposition or proposed explanation made on the basis of limited evidence as a starting point for further investigation.
That's a good, simple description of a "hypothesis".
Another way to describe it is "an educated guess".
Once you have it in words, it's time to start checking it out, with experiments that can show whether it's true or not.
If your experiments seem to show that your hypothesis seems to be true, that doesn't 'prove' it, but you can start calling your hypothesis a "theory".
(It's possible that you may never be able to 'prove' it. It may remain a theory forever. Like gravity, germs, atoms, and relativity. Thousands of successful experiments don't 'prove' a theory, but it can be trashed by one good, valid experiment to show that it's false.)
Two mechanical waves intersect and produce the straight line seen here. What is the result of this intersection called?
Answer:constructive interfrence
Explanation:
The driver of a truck has an acceleration of 0.3 g as the truck passes over the top of a hump in the road at a constant speed. The radius of curvature of the road at the top of the road is 98 m, and the center of mass G of the driver, who can be considered a particle, is 2 m above the road. What is the speed of the truck
Answer:
17.115m/s
Explanation:
The formula that will be used to calculate the speed of the truck is expressed as shown:
v = √ar
a is the acceleration of the truck
r is the radius of curvature of the road at the top of the road plus centre of mass G who can be considered a particle, is 2 m
v = √a(R+G)
Given parameters
a = 0.3g (g is the acceleration due to gravity)
R = 98m
G = 2m
Substituting the values into the formula:
v = √0.3(9.81){98+2}
v = √0.3×9.81×100
v = √294.3
v = 17.155m/s
Hence the speed of the truck is 17.155m/s
Suppose that a particle accelerator is used to move two beams of particles in opposite directions. In a particular region, electrons move to the right at 7130 m/sand protons move to the left at 2583 m/s. The particles are evenly spaced with 0.0288 m between electrons and 0.0747 m between protons. Assuming that there are no collisions and that the interactions between the particles are negligible, what is the magnitude of the average current in this region?
Answer:
Total current, [tex]I=4.51\times 10^{-14}\ A[/tex]
Explanation:
Velocity of electrons is 7130 m/s and particles are evenly spaced with 0.0288 m between electrons. We can find no of electrons passing per second as follows :
[tex]n_e=\dfrac{7130\ m/s}{0.0288\ m}\\\\n_e=247569.44[/tex]
Velocity of protons is 2583 m/s and particles are evenly spaced with 0.0747 m between electrons. We can find no of protons passing per second as follows :
[tex]n_p=\dfrac{2583 \ m/s}{0.0747 \ m}\\\\n_p=34578.31[/tex]
Total current in this region is equal to sum of current due to electrons and current due to protons.
[tex]I=n_e\times e+n_p\times e\\\\I=e(n_e+n_p)\\\\I=1.6\times 10^{-19}\times (247569.44+34578.31)\\\\I=4.51\times 10^{-14}\ A[/tex]
Hence, this is the required solution.
The symbol equation below is used to calculate distance travelled. Rearrange this symbol equation so you could use it to calculate the speed instead. s = v t
Answer:
Below
Explanation:
s = Distance
v = Velocity ( speed)
t = time
[tex]s = vt[/tex]
Divide both sides of the equation by t
[tex] \frac{s}{t} = \frac{vt}{t} \\ \frac{s}{t} = v[/tex]
11.50 kg object has the given and acceleration components. =(0.35ms2)+(0.73ms3) =(11.5ms2)−(0.75ms3)
