Answer:16.5 m/s
Explanation:
Given
Velocity of boy![(v_b)=4.3 m/s](https://tex.z-dn.net/?f=%28v_b%29%3D4.3%20m%2Fs)
velocity of girl![(v_g)=8.8 m/s](https://tex.z-dn.net/?f=%28v_g%29%3D8.8%20m%2Fs)
velocity of ball relative to boy
backward
Now We have to find velocity of ball relative to girl
Representing it in vector form
![v_b=4.3\hat{i}](https://tex.z-dn.net/?f=v_b%3D4.3%5Chat%7Bi%7D)
![v_g=8.8\hat{i}](https://tex.z-dn.net/?f=v_g%3D8.8%5Chat%7Bi%7D)
![v_{Bb}=-11.4\hat{i}](https://tex.z-dn.net/?f=v_%7BBb%7D%3D-11.4%5Chat%7Bi%7D)
and
![v_{Bb}=v_B-v_b](https://tex.z-dn.net/?f=v_%7BBb%7D%3Dv_B-v_b)
![v_B=v_{Bb}+v_b](https://tex.z-dn.net/?f=v_B%3Dv_%7BBb%7D%2Bv_b)
![v_B=-11.4\hat{i}+4.3\hat{i}=-7.1\hat{i}](https://tex.z-dn.net/?f=v_B%3D-11.4%5Chat%7Bi%7D%2B4.3%5Chat%7Bi%7D%3D-7.1%5Chat%7Bi%7D)
therefore velocity of ball relative to girl
![v_{Bg}=v_B-v_g=-7.1\hat{i}-8.8\hat{i}=-16.5\hat{i}](https://tex.z-dn.net/?f=v_%7BBg%7D%3Dv_B-v_g%3D-7.1%5Chat%7Bi%7D-8.8%5Chat%7Bi%7D%3D-16.5%5Chat%7Bi%7D)
Explanation:
Draw free body diagrams for each mass.
There are 3 forces on the disk: weight force mg pulling down, normal force N pushing up, and tension force T pulling right.
There are 2 forces on the cylinder: tension force T pulling up and weight force 3mg pulling down.
Sum of forces on the disk in the centripetal direction:
∑F = ma
T = m v²/r
Sum of forces on the cylinder in the vertical direction:
∑F = ma
T − 3mg = 0
T = 3mg
Substituting:
3mg = m v²/r
3gr = v²
v = √(3gr)
Plug in values:
v = √(3 × 10 m/s² × 0.800 m)
v = √24 m/s
v ≈ 4.90 m/s
A is the best choice!!!!!!!