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3 years ago

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During a tennis serve, a racket is given an angular acceleration of magnitude 155 rad/s2. At the top of the serve, the racket ha

s an angular speed of 20.0 rad/s. If the distance between the top of the racket and the shoulder is 1.40 m, find the magnitude of the total acceleration of the top of the racket.

1 answer:

Inessa05 [86]3 years ago

6 0

Answer:

600.6 m/s^2

Explanation:

α = 155 rad/s^2

ω = 20 rad/s

r = 1.4 m

Tangential acceleration, aT = r x α = 1.4 x 155 = 217 m/s^2

Centripetal acceleration, ac = rω^2 = 1.4 x 20 x 20 = 560 m/s^2

The tangential acceleration and the centripetal acceleration both are perpendicular to each other. Let a be the resultant acceleration.

a^2 = aT^2 + ac^2

a^2 = 217^2 + 560^2

a = 600.6 m/s^2

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An object is projected at 25m/s from the top of a building of height 50m. At the same instant,another object is projected from t

docker41 [41]

A) The objects have the same vertical position after 2 seconds

B) The objects have same vertical position at y = 30.4 m (but they do not collide since they have different x-position)

Explanation:

The motion of the first object along the vertical direction is a uniformly accelerated motion, so we can write its position at time t using the following equation:

$y_1(t)=h+u_1 t + \frac{1}{2}gt^2$

where:

h = 50 m is the initial height

$u_1=0$ is the initial vertical velocity (the object is projected horizontally, so the vertical velocity is zero at the beginning)

$g=-9.8 m/s^2$ is the acceleration of gravity

So, its vertical position can be rewritten as

$y_1(t)=50-4.9t^2$

The position of object 2 instead can be written as

$y_2(t)=(u_2 sin \theta)t + \frac{1}{2}gt^2$

where

$u_2 sin \theta$ is the initial vertical velocity, where

$u_2 = 50 m/s$ is the initial velocity

$\theta=30^{\circ}$ is the angle of projection

Substituting, we get:

$y_2(t)=(50)(sin 30^{\circ})t+\frac{1}{2}(-9.8)t^2=25t-4.9t^2$

The two objects collide when their vertical position is the same, so:

$y_1(t)=y_2(t)\\50-4.9t^2 = 25t-4.9t^2$

And solving for t, we find:

$50=25t\\t= 2 s$

Note that this means that the two object at t = 2 s have the same vertical position: however, this is not true for the horizontal position.

B)

In order to find the point where they collide, we have to substitute the time of the collision that we found in part A into one of the expressions of the vertical position.

Substituting into the expression of object 2, we find:

$y_2(t) = 25t-4.9t^2=25(2.0)-4.9(2.0)^2=30.4 m$

We can verify that at the same time, the vertical position of object 1 is the same:

$y_1(t)=50-4.9t^2=50-4.9(2.0)^2=30.4 m$

This means that the two objects have the same vertical position at 30.4 m.

However, in reality, the two objects do not collide. In fact, object 1 is moving in the horizontal direction with constant velocity

$v_{1x}=25 m/s$

So its horizontal position at t = 2.0 s is

$x_1(2.0)=v_{1x}t=(25)(2.0)=50 m$

While object 2 is moving in the horizontal plane with velocity

$v_{2x}=u_2 cos \theta=(50)(cos 30^{\circ})=43.3 m/s$

So its horizontal position at t = 2.0 s is

$x_2(2.0)=v_{2x}t=(43.3)(2.0)=86.6 m$

So in reality, the two objects do not collide, if they start from the same x-position.

Learn more about projectile motion:

brainly.com/question/8751410

#LearnwithBrainly

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3 years ago

Why is it called a compound light microscope?

irina [24]

They are desighned with multiple lenses

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4 years ago

To initiate a nuclear reaction, an experimental nuclear physicist wants to shoot a proton into a 5.50-fm-diameter 12C nucleus. T

Crazy boy [7]

Answer:

The value is $u = 3.23 *10^{7} \ m/s$

Explanation:

From the question we are told that

The diameter of the nucleus is $d = 5.50 \ fm = 5.50 *10^{-15} \ c$

The charge of the proton that makes up the nucleus is $Q_2 = \frac{12}{2} * 1.60 *10^{-19} =9.6*10^{-19} \ C$

The energy to be impacted is $KE_f = 2.30 \ MeV = 2.30 *10^{6} \ eV = 2.30 *10^{6} * 1.60 *10^{-19} = 3.68*10^{-13} \ J$

Generally the radius of the nucleus is mathematically represented as

$r = \frac{d}{2}$

=> $r = \frac{5.50 *10^{-15}}{2}$

=> $r = 2.75 *10^{-15} \ m$

Generally from the law energy conservation we have that

$Initial \ total \ energy \ of the \ proton = final \ total \ energy \ of the \ proton$

i.e

$T_i = T_f$

Here

$T_i = KE_i + PE_i$

Here $KE_i$ is the initial kinetic energy which is mathematically represented as

$KE_I = \frac{1}{2} * m * u ^2$

Here $PE_i$ is the initial potential energy of the proton and the value is 0 J given that the proton is moving

Also $T_f$ is mathematically represented as

$T_f = KE_f + PE_f$

Here

$PE_f$ is the final potential energy which is mathematically represented as

$PE_f = \frac{k * Q_1 * Q_2}{r}$

Here $Q_1$ is the charge on the proton with a value of $Q_1 = 1.60 *10^{-19} \ C$

So

$PE_f = \frac{9*10^{9} *(1.60 *10^{-19} ) * ( 9.6 *10^{-19})}{ 2.75 *10^{-15}}$

=> $PE_f = 5.027 *10^{-13 } \ J$

So

$KE_i + PE_i = KE_f + PE_f$

=> $\frac{1}{2} * m * u ^2 +0 = 3.68*10^{-13} + 5.027 *10^{-13 }$

Here m is the mass of the moving proton with value $m = 1.67*10^{-27} \ kg$

So

$\frac{1}{2} * 1.67*10^{-27} * u ^2 +0 = 3.68*10^{-13} + 5.027 *10^{-13 }$

=> $u = \sqrt{\frac{3.68*10^{-13} + 5.027 *10^{-13 }}{0.5 * 1.67*10^{-27}} }$

=> $u = 3.23 *10^{7} \ m/s$

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3 years ago

Since velocity describes both speed and direction you can call it

Fittoniya [83]

Since velocity describes both speed and direction, you can call it a "vector" quantity, and legitimately label it "velocity".

Since speed has no direction, it's a scalar quantity, and it's wrong to call it "velocity" as so many often do.

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4 years ago

Which of the following is the best example of Newton's second law of motion?

Alex_Xolod [135]

Answer:

C. A baseball bat strikes a baseball.

Explanation:

Newton's second law of motion states that acceleration happens when force is applied on the mass.

<em>A baseball bat strikes a baseball is the best example of Newton's second law of motion because acceleration of the baseball is directly proportional to the force by which baseball bat hit it.</em>

Hence, the correct option is 'C. A baseball bat strikes a baseball.'

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3 years ago

Read 2 more answers