Two vectors having magnitudes of 5.00 and 9.00 respectively. If the value of their dot product is 12.0, find the angle between the two vectors. ​

Answer:

30 minutes

Explanation:

Energy per time is constant, so:

E₁ / t₁ = E₂ / t₂

m₁C₁ΔT₁ / t₁ = m₂C₂ΔT₂ / t₂

(1 kg) C (70°C − 25°C) / 15 min = (1.5 kg) C (80°C − 20°C) / t

(1 kg) (45°C) / 15 min = (1.5 kg) (60°C) / t

3/min = 90 / t

t = 30 min

Answer:

e. 400 Hz

Explanation:

In closed organ pipe,  only odd harmonics of fundamental note is possible .

The fundamental frequency is 200 Hz . Then other overtones will be having following frequencies .

200 x 3 , 200 x 5 , 200 x 7 , 200 x 9 etc

600 Hz , 1000 Hz , 1400 Hz  , 1800 Hz .

Frequency not possible is 400 Hz .

Answer:

A. Final Floor = 15.5 = 15 (Considering downward portion of elevator)

B. T = 14859.5 N = 14.89 KN

Explanation:

A.

First we calculate distance covered by the elevator during downward motion. Downward motion consists of two parts. First one is uniformly accelerated. For that part we use 2nd equation of motion:

s₁ = Vi t + (0.5)at²

where,

s₁ = distance covered during accelerated downward motion = ?

Vi = initial speed = 0 m/s (since elevator is initially at rest)

t = time taken = 6 s

a = acceleration = 1.5 m/s²

Therefore,

s₁ = (0 m/s)(6 s) + (0.5)(1.5 m/s²)(6 s)²

s₁ = 4.5 m

also we find the final velocity using 1st equation of motion:

Vf = Vi + at

Vf = 0 m/s + (1.5 m/s²)(6 s)

Vf = 9 m/s

Now, the second part of downward motion is with constant velocity. So:

s₂ = vt

where,

s₂ = distance covered during constant speed downward motion = ?

v = Vf = 9 m/s

t = 6 s

Therefore,

s₂ = (9 m/s)(6 s)

s₂ = 54 m

Now for distance covered during upward motion is given by the 2nd equation of motion. Since the values of acceleration and time are same. Therefore, it will be equal in magnitude to s₁:

s₃ = s₁ = 4.5 m

Therefore, the total distance covered by elevator is given by following equation:

s = s₁ + s₂ - s₃      (Downward motion taken positive)

s = 4.5 m + 54 m - 4.5 m

s = 54 m

Therefore, net motion of the elevator was 54 m downwards.

So the final floor will be:

Final Floor = Initial Floor - Distance Covered/Length of a floor

Final Floor = 29 - 54 m/4m

Final Floor = 15.5 = 15 (Considering the downward portion or floor of elevator)

B.

The maximum tension will occur during the upward accelerated motion. It is given by the formula:

T = m(g + a)

where,

T = Max. Tension in Cable = ?

m = total mass of person and elevator = 115 kg + 1200 kg = 1315 kg

g = 9.8 m/s²

a = acceleration = 1.5 m/s²

Therefore,

T = (1315 kg)(9.8 m/s² + 1.5 m/s²)

T = 14859.5 N = 14.89 KN

Answer:

887.2 N

Explanation:

Given that

Mass of Lara, m = 62 kg

Length of the vine, l = 8.8 m

Speed of the swing, v = 6.3 m/s Then,

We start by calculating her weight.

w = mass * acceleration

w = mg

w = 62 * 9.8

w = 607.6 N

F(c) = mv²/l, on substituting

F(c) = (62 * 6.3²) / 8.8

F(c) = 2460.78 / 8.8

F(c) = 279.6 N

T - 607.6 N = 279.6 N

T = 607.6 N + 279.6 N

T = 887.2 N

Thus, the minimum breaking strength of the vine is 887.2 N

The minimum breaking strength of the vine is about 900N.

Tension is a force developed by a rope, string, or cable when stretched under an applied force.

Given:

Mass (m) = 62 kg, length (l) = 8.8 m, velocity (v) = 6.3 m/s, g = 10 m/s².

Weight(W) = m * g = 62 * 10 = 620N

centripetal force = F(c) = mv²/l = 62 * 6.3² / 8.8 = 279.6N

T - W = F(c)

T - 620 = 279.6

T = 900N

The minimum breaking strength of the vine is about 900N.

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Answer:

none of the answers is correct, the time  is the same  t₁ = t₂ = 0.600 s

Explanation:

This is a kinematics exercise, analyze the situation a bit. The vertical speed in both cases is the same is zero, the horizontal speed in the second case is double (vₓ₂ = 2 vₓ₁)

let's find the time to hit the ground

     y = y₀ + I go t - ½ g t²

     0 = y₀ - ½ g t²

     t = √ 2y₀ / g

with the data from the first launch

     y₀i = ½ g t²

     y₀ = ½  9.8  0.6²

     y₀ = 1,764 m

with this is the same height the time to descend in the second case is the same

    t₂ = 0.600 s

this is because the horizontal velocity change changes the offset on the x axis, but does not affect the offset on the y axis

Therefore, none of the answers is correct, the time  is the same

t₁ = t₂ = 0.600 s

Answer:

d

Explanation:

good question. now the bus is moving in constant velocity . a student in front tosses a ball to the student in back. but we dont know the speed at which the student tosses a ball. we have to assume the speed

assume the speed of ball is slightly less than the speed of bus. in this case the stationary observer sees the ball in slower speed than the one inside the bus.

so a is correct

now assume the speed of ball is 1/2 the speed of bus. here stationary observer sees the ball the same speed as the one in bus observe

b is correct

assume the speed of ball is very small than the speed of bus . in this case the stationary observer see in grater speed than the student in bus

e also correct

so correct answer is d. it depends on the speed of ball tossed by the student in front.

Answer:

If the acceleration is constant, the movements equations are:

a(t) = A.

for the velocity we can integrate over time:

v(t) = A*t + v0

where v0 is a constant of integration (the initial velocity), for the distance traveled between t = 0 units and t = 10 units, we can solve the integral:

[tex]\int\limits^{10}_0 {A*t + v0} \, dt = ((A/2)10^2 + v0*10) = (A*50 + v0*10)[/tex]

Where to obtain the actual distance you can replace the constant acceleration A and the initial velocity v0.

Answer:

The lifetime of the particle is  [tex]\Delta t = 2.6*10^{-25} \ s[/tex]

Explanation:

From the question we are told that

    The average rest energy is [tex]E = 91.19 \ GeV = 91.19GeV * \frac{1.60 *10^{-10} J }{1GeV} = 1.46 *10^{-8}J[/tex]

    The intrinsic width is  [tex]\Delta E =2.5eV = 2.5GeV * \frac{1.60 *10^{-10}J }{1GeV} = 4*10^{-10} J[/tex]

The lifetime is mathematically represented as

     [tex]\Delta t = \frac{h}{\Delta E}[/tex]

Where h is the Planck's constant with a value of  [tex]1.055*10^{-34} \ J\cdot s[/tex]  

substituting values

    [tex]\Delta t = \frac{1.055*10^{-34}}{4 *10^{-10}}[/tex]

     [tex]\Delta t = 2.6*10^{-25} \ s[/tex]

Complete Question

An airplane takes off a runway at a constant speed of 49 m/s at constant angle 30 to the horizontal.How high (in meters )  is the airplane above the ground 13 seconds after takeoff?

Answer:

The height  is [tex]H = 318.5 \ m[/tex]

Explanation:

From the question we are told that

   The speed at which the plane takes off is  [tex]u = 49 \ m/s[/tex]

      The angle at which it takes off is  [tex]\theta = 30 ^o[/tex]

        The time taken is [tex]t = 13 s[/tex]

The vertical distance traveled is  mathematically represented as

          [tex]H = u sin \theta t[/tex]

Substituting values  

         [tex]H = (49) * sin (30) *13[/tex]

        [tex]H = 318.5 \ m[/tex]

Answer:

  a) -5.26 m/s

  b) 27.91 m

Explanation:

a) The acceleration due to gravity makes the velocity increase in magnitude in a linear way. The average velocity over the interval will be equal to the actual velocity halfway through the interval. The velocity at the beginning of the interval will be higher (less negative) by the amount velocity changes in the first half of the interval.

  average velocity = (0 -(26.5 m))/(1.85 s) ≈ -14.324 m/s

The change in velocity in the first half of the interval is ...

  Δv = (Δt/2)×(-9.8 m/s²) = (1.85 s)(-4.9 m/s²) = -9.065 m/s

So, the initial velocity (at the beginning of the last 1.85 s interval) is ...

  v1 = (average velocity) -Δv = (-14.324 m/s) -(-9.065 m/s)

  v1 = -5.259 m/s

__

b) The velocity when the object hits the ground is ...

  v2 = average velocity +Δv = -14.324 m/s -9.065 m/s = -23.389 m/s

This is related to the distance traveled by ...

  v² = 2dg . . . . . where g is the acceleration and d is the distance traveled

  d = v²/(2g) = 23.389²/(2·9.8) = 27.911 . . . . meters

The object travels a total distance of about 27.911 meters.

_____

The attached graph shows height vs. time.

Answer:

Some of the advantages if our body had magnetic properties are as follows:

Hence, magnetic properties are somehow beneficial for humans.  

Answer:

The volume of the marble is [tex]523.33\ mm^2[/tex].

Explanation:

Marble is spherical in shape. The diameter of marble is 10 mm. It radius will be 5 mm.

The volume of spherical shaped object is given by :

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

Plugging all the values, we get :

[tex]V=\dfrac{4}{3}\times 3.14\times (5)^3\\\\V=523.33\ mm^2[/tex]

So, the volume of the marble is [tex]523.33\ mm^2[/tex].

Answer:

  k = 6,547 N / m

Explanation:

This laboratory experiment is a simple harmonic motion experiment, where the angular velocity of the oscillation is

         w = √ (k / m)

angular velocity and rel period are  related

         w = 2π / T

substitution

         T = 2π √(m / K)

in Experimental measurements give us the following data

  m (g)     A (cm)    t (s)   T (s)

  100        6.5         7.8    0.78

  150        5.5          9.8   0.98

   200      6.0        10.9    1.09

   250       3.5        12.4    1.24

we look for the period that is the time it takes to give a series of oscillations, the results are in the last column

        T = t / 10

To find the spring constant we linearize the equation

        T² = (4π²/K)    m

therefore we see that if we make a graph of T² against the mass, we obtain a line, whose slope is

         m ’= 4π² / k

where m’ is the slope

           k = 4π² / m'

the equation of the line of the attached graph is

       T² = 0.00603 m + 0.0183

therefore the slope

       m ’= 0.00603  s²/g

    we calculate

         k = 4 π² / 0.00603

          k = 6547 g / s²

we reduce the mass to the SI system

         k = 6547 g / s² (1kg / 1000 g)

         k = 6,547 kg / s² =

         k = 6,547 N / m

let's reduce the uniqueness

         [N / m] = [(kg m / s²) m] = [kg / s²]

The spring-mass system forms a linear graph between the time period and mass. And the value of spring-constant from the given data is 6.46 N/m.

Given data:

Mass suspended by spring is, [tex]m=100 \;\rm g =0.1 \;\rm kg[/tex].

Number of oscillations is, [tex]n =10\;\rm oscillations[/tex].

Time period of oscillation is, [tex]T=7.8 \;\rm s[/tex].

The expression for the angular frequency of spring-mass system is,

[tex]\omega =\drac \sqrt{\dfrac{k}{m} }[/tex]  ......................................................(1)

Here, k is the spring constant.

Angular frequency is also expressed as,

[tex]\omega = 2 \pi f[/tex] .........................................................(2)

here, f is the linear frequency of spring-mass system.

And linear frequency is,

[tex]f=\dfrac{n}{T}\\f=\dfrac{10}{7.81}\\f=1.28 \;\rm cycles/sec[/tex]

Then substitute equation (2) in equation (1) as,

[tex]2 \pi f=\drac \sqrt{\dfrac{k}{m} }\\2 \pi \times 1.28=\drac \sqrt{\dfrac{k}{0.1} }\\(2 \pi \times 1.28)^{2}= \dfrac{k}{0.1}\\k = 6.46 \;\rm N/m[/tex]

Thus, the value of spring constant is 6.46 N/m. And the suitable graph for the spring-mass system is given below.

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Answer:

rt

Explanation:

Answer:

Hope this helps :)

Explanation:

1. A

2. G (because the basic definition of internal energy is, the sum of kinetic and potential energies of water molecules)

Answer:

General Expression: E = kql/(l² + r²)^(3/2)

(a) 6.3 MN/C

(b) 22.8 MN/C

(c) 6.1 MN/C

(d) 0.63 MN/C

Explanation:

The general expression for electric field along axis of a uniformly charged ring is:

E = kqL/(L² + r²)^(3/2)

where,

E = Electric Field Strength = ?

k = Coulomb's Constant = 9 x 10⁹ N.m²/C²

q = Total Charge = 71 μC = 71 x 10⁻⁶ C

L = Distance from center on axis

r = radius of ring = 10 cm = 0.1 m

(a)

L = 1 cm = 0.01 m

Therefore,

E = (9 x 10⁹ N.m²/C²)(71 x 10⁻⁶ C)(0.01 m)/[(0.01 m)² + (0.1 m)²]^(3/2)

E = (6390 N.m³/C)/(0.00101 m³)

E =  6.3 x 10⁶ N/C = 6.3 MN/C

(b)

L = 5 cm = 0.05 m

Therefore,

E = (9 x 10⁹ N.m²/C²)(71 x 10⁻⁶ C)(0.05 m)/[(0.05 m)² + (0.1 m)²]^(3/2)

E = (31950 N.m³/C)/(0.00139 m³)

E =  22.8 x 10⁶ N/C = 27.4 MN/C

(c)

L = 30 cm = 0.3 m

Therefore,

E = (9 x 10⁹ N.m²/C²)(71 x 10⁻⁶ C)(0.3 m)/[(0.3 m)² + (0.1 m)²]^(3/2)

E = (191700 N.m³/C)/(0.03162 m³)

E =  6.1 x 10⁶ N/C = 6.1 MN/C

(d)

L = 100 cm = 1 m

Therefore,

E = (9 x 10⁹ N.m²/C²)(71 x 10⁻⁶ C)(1 m)/[(1 m)² + (0.1 m)²]^(3/2)

E = (639000 N.m³/C)/(1.015 m³)

E =  0.63 x 10⁶ N/C = 0.63 MN/C

Explanation:

P=W/T ==> 1000w = Q/600 ==> Q=600000j

If a 1 - kilowatt electric heater is switched on for ten minutes then the heat produced by the electric heater would be 600 - kilo Joules .

It can be defined as the form of the energy in which heat is transferred from one body to another body due to their molecular movements, thermal energy is also known as heat energy .

As given in the problem , we have to find out the heat produced by the 1 -  kilo watts electric heater if it is switched on for ten minutes ,

The heat produced by the electric heater = Power × time

                                                                      = 1000 × 600 Joules

                                                                      = 600 kilo - Joules

Thus , the heat produced by the electric heater would be 600 - kilo Joules .

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Answer:

d = 3.5*10^4 m

Explanation:

In order to calculate the displacement of the airplane you need only the information about the initial position and final position of the airplane. THe initial position is at the origin (0,0,0) and the final position is given by the following vector:

[tex]\vec{r}=(1.21*10^3\hat{i}+3.45*10^4\hat{j})m[/tex]

The displacement of the airplane is obtained by using the general form of the Pythagoras theorem:

[tex]d=\sqrt{(x-x_o)^2+(y-y_o)^2}[/tex]   (1)

where x any are the coordinates of the final position of the airplane and xo and yo the coordinates of the initial position. You replace the values of all variables in the equation (1):

[tex]d=\sqrt{(1.12*10^3-0)^2+(3.45*10^4-0)^2}=3.45*10^4m[/tex]

hence, the displacement of the airplane is 3.45*10^4 m

Answer:

The correct answer is C 1, 4, and 5 tie, then 2 and 3 tie

Explanation:

Solution

The electric field due to sheets E₁ positive =б/2E₀

E₂ is negative = б/2E₀

Now,

At the point 1, 4, 5 the electric field due to the sheets are in the opposite direction

At the point 1, the net field = -E₁ + E₂ =0

At the point A, the net field = -E₁ - E₂ = 0

Now,

At nay point inside between them, the electric field is seen to be at the same direction.

At the 2, 3 points the field is seen at the right

Thus,

E net = E₁ + E₂

= б/2E₀ + σ/2E₀

=б/E₀

Note: Kindly find an attached copy of the complete question to the solution

The correct answer is option C

The rank of the points according to the magnitude of the electric field is 1, 4, and 5 tie, then 2 and 3 tie

Let sheet 1 has positive surface charge density and sheet 2 has a negative surface charge density

The electric field (without direction) due to sheets will be

E₁ =σ/2E₀

E₂= σ/2E₀

Now,

At the point 1, 4, 5 the electric field due to the sheets is given by:

E = E₁ - E₂

E = σ/2E₀ - σ/2E₀

since the positive charge plate will have electric field lines away from the sheet and the negative charge plate will have electric field lines towards the sheet

E = 0

Now,

At points 2, 3 which are between the plates,

The net electric field is:

E = E₁ + E₂

since the electric field due to both the plates will be from positive to negative ( towards the negatively charged plate)

E = σ/2E₀ + σ/2E₀

E = σ/E₀

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Answer:

Explanation: please see attached file I attached the answer to your question.

The angle between the magnetic field and the wire's velocity is 33.2 degrees.

Since the potential difference = 71mv = 71 *10 ^-3 V

The length is 12 cm = 0.12m

The magnetic field i.e. B = 0.27T

The speed or v = 4 m/s

here we assume [tex]\theta[/tex] be the angle

So,

e = Bvl sin[tex]\theta[/tex]

So,

[tex]Sin\theta[/tex] = e/bvl

= 71*10^-3 / 0.27 *4*0.12

= 0.5478

= 33.2 degrees

Therefore, the angle should be 33.2 degrees

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Answer:

The actual height is  [tex]A =3.158 \ m[/tex]

Explanation:

From the question we are told that

   The depth of the person is  [tex]d = 1.1 \ m[/tex]

    The apparent height  is  [tex]D = 4.2 \ m[/tex]

Generally

     The refractive index of water is  [tex]n_w = 1.33[/tex]

      The refractive index of the air is  [tex]n_a = 1[/tex]

The apparent depth is mathematically represented as

      [tex]D = A [\frac{n_w}{n_a} ][/tex]  

substituting values

     [tex]4.2 = A [\frac{1.33}{1} ][/tex]  

=>   [tex]A = \frac{4.2 }{1.33}[/tex]

      [tex]A =3.158 \ m[/tex]

The ball was dropped at the height of "3.158 m". To understand the calculation, check below.

According to the question,

Water's refractive index, [tex]n_w[/tex] = 1.33

Air's refractive index, [tex]n_a[/tex] = 1

Apparent height, D = 4.2 m

Person's depth, d = 1.1 m

We know the relation,

→ D = A[[tex]\frac{n_w}{n_a}[/tex]]

By substituting the values, we get

4.2 = A[[tex]\frac{1.33}{1}[/tex]]

By applying cross-multiplication,

  A = [tex]\frac{4.2}{1.33}[/tex]

      = 3.158 m

Thus the approach above is correct.

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Answer:

Force = 60.08 N

Explanation:

Given that

Diameter d = 30 mm  

Holding pressure = 85 %  of Atmospherics pressure

Solution

As we know that  here 1 atm = 10⁵ N/m²

and pressure is known as force per unit area

pressure = [tex]\frac{F}{A}[/tex]   ................1

put here value and we will get

F = [tex]0.85\times 10^5\times \frac{\pi}{4}\times 0.03^2\ N[/tex]

solve it we get

Force = 60.08 N

Answer:

Explanation:

angular momentum of the putty about the point of rotation

= mvR   where m is mass , v is velocity of the putty and R is perpendicular distance between line of velocity and point of rotation .

= .045 x 4.23 x 2/3 x .95 cos46

= .0837 units

moment of inertia of rod = ml² / 3 , m is mass of rod and l is length

= 2.95 x .95² / 3

I₁ = .8874 units

moment of inertia of rod + putty

I₁ + mr²

m is mass of putty and r is distance where it sticks

I₂  = .8874 + .045 x (2 x .95 / 3)²

I₂ = .905

Applying conservation of angular momentum

angular momentum of putty = final angular momentum of rod+ putty

.0837 = .905 ω

ω is final angular velocity of rod + putty

ω = .092 rad /s .

Answer:

1.25 m/s^2

Explanation:

F = m*a ...... force = mass * acceleration

force = 100 N, mass = 80 kg

100 = 80 * a

100/80 = a = 1.25 m/s^2

Answer:

The acceleration is 1.25m/s².

Explanation:

You have to apply Newton's Second Law which is F = m×a where F represents force, m is mass and a is acceleratipn. Then you have to substitute the following values into the formula :

[tex]f = m \times a[/tex]

Let F = 100,

Let m = 80,

[tex]100 = 80 \times a[/tex]

[tex]100 = 80a[/tex]

[tex]a = 100 \div 80[/tex]

[tex]a = 10 \div 8[/tex]

[tex]a = 1.25[/tex]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The correct option is  B

Explanation:

The system is best considered a closed system because looking at process we can see that there was no exchange of matter between the system and the surrounding,(as the was no escape of matter from the system to the surrounding )

Secondly we can  deduce that there is  a variation in the volume. from [tex]1.0 m^3[/tex] to [tex]0.5 m^3[/tex]

Answer :v=480m400s=1.2ms

2002+4802=H2  

The hypotenuse  H=520m  

A quicker way to get the length of the hypotenuse is to recognize that this is a simple 5–12–13 triangle where the sides are multiples of 5, 12, and 13:

5(40) = 200m, 12(40)= 480m, 13(40)= 520m

We know that the swimmer travelled 520 m in 400 seconds, so her average speed was:

VR=520m400sec=   1.3ms

hope i got it right!! xx

Explanation:

Answer:

A burning candle. (chemical energy into energy of heat and light, i.e. thermal and wave)

Explanation:

Answer:

Explanation shown below.

Explanation:

1.The number of images formed by 2 parallel mirrors is an infinite number of images.

2. The characteristics of a plane mirror is such that the object distance equals the image distance.

Hence the object distance is 8.7cm from the right; the image formed would be 8.7cm behind the mirror.

Now a second image is going to be formed by the left mirror which is going to have an image distance of 30.1cm behind the mirror.

Now this image would be reflected on the right side to form a new image which is going to be seen as 38.8 +30.1 = 68.9cm behind the right Mirror .

Hence the shortest distances are 8.7cm and 68.9cm

3. The number of reflections is infinite for both cases.