On the list of choices that you provided, there is no such statement.
Answer:
![W_f = 2.319 rad/s](https://tex.z-dn.net/?f=W_f%20%3D%202.319%20rad%2Fs)
Explanation:
For answer this we will use the law of the conservation of the angular momentum.
![L_i = L_f](https://tex.z-dn.net/?f=L_i%20%3D%20L_f)
so:
![I_mW_m = I_sW_f](https://tex.z-dn.net/?f=I_mW_m%20%3D%20I_sW_f)
where
is the moment of inertia of the merry-go-round,
is the initial angular velocity of the merry-go-round,
is the moment of inertia of the merry-go-round and the child together and
is the final angular velocity.
First, we will find the moment of inertia of the merry-go-round using:
I = ![\frac{1}{2}M_mR^2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7DM_mR%5E2)
I = ![\frac{1}{2}(115 kg)(2.5m)^2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28115%20kg%29%282.5m%29%5E2)
I = 359.375 kg*m^2
Where
is the mass and R is the radio of the merry-go-round
Second, we will change the initial angular velocity to rad/s as:
W = 0.520*2
rad/s
W = 3.2672 rad/s
Third, we will find the moment of inertia of both after the collision:
![I_s = \frac{1}{2}M_mR^2+mR^2](https://tex.z-dn.net/?f=I_s%20%3D%20%5Cfrac%7B1%7D%7B2%7DM_mR%5E2%2BmR%5E2)
![I_s = \frac{1}{2}(115kg)(2.5m)^2+(23.5kg)(2.5m)^2](https://tex.z-dn.net/?f=I_s%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28115kg%29%282.5m%29%5E2%2B%2823.5kg%29%282.5m%29%5E2)
![I_s = 506.25kg*m^2](https://tex.z-dn.net/?f=I_s%20%3D%20506.25kg%2Am%5E2)
Finally we replace all the data:
![(359.375)(3.2672) = (506.25)W_f](https://tex.z-dn.net/?f=%28359.375%29%283.2672%29%20%3D%20%28506.25%29W_f)
Solving for
:
![W_f = 2.319 rad/s](https://tex.z-dn.net/?f=W_f%20%3D%202.319%20rad%2Fs)
The horizontal force applied is 160 N while the velocity is 2.03 m/s.
<h3>What is the speed of the car?</h3>
The work done by the car is obtained as the product of the force and the distance;
W = F x
F = ?
x = 30.0 m
W = 4,800 J
F = 4,800 J/30.0 m
F = 160 N
But F = ma
a = F/m
a = 160 N/2.30 ✕ 10^3-kg
a= 0.069 m/s
Now;
v^2 = u^2 + 2as
u = 0/ms because the car started from rest
v = √2as
v = √2 * 0.069 * 30
v = 2.03 m/s
Learn more about force and work:brainly.com/question/758238
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