Question

A ball of mass 0.5kg is thrown at a man of mass 59.5kg standing on roller skates, at a speed of 5 m/s. It is stopped by the man. What is the velocity of the man with the ball?

Answer 1

The final velocity of the man standing on roller skates with the ball caught, after it is thrown at him at a speed of 5 m/s, is 0.042 m/s.                        

 

The velocity of the man with the ball can be calculated by conservation of linear momentum:

$p_{i} = p_{f}$

$m_{b}v_{b_{i}} + m_{m}v_{m_{i}} = m_{b}v_{b_{f}} + m_{m}v_{m_{f}}$

Where:

$m_{b}$: is the mass of the ball = 0.5 kg

$m_{m}$: is the mass of the man = 59.5 kg

$v_{b_{i}}$: is the initial velocity of the ball = 5 m/s

$v_{m_{i}}$: is the initial velocity if the man = 0 (he is standing still)

$v_{b_{f}}$: is the final velocity of the ball =?

$v_{m_{f}}$: is the final velocity of the man =?

Since the man catches the ball, his final velocity is the same that the final ball's velocity, so:

$m_{b}v_{b_{i}} + m_{m}v_{m_{i}} = v_{f}(m_{b} + m_{m})$

$v_{f} = \frac{m_{b}v_{b_{i}} + m_{m}v_{m_{i}}}{m_{b} + m_{m}} = \frac{0.5 kg*5 m/s + 0}{0.5 kg + 59.5 kg} = 0.042 m/s$

Therefore, the velocity of the man with the ball is 0.042 m/s.

Learn more about the conservation of linear momentum here:  

• brainly.com/question/2141713?referrer=searchResults

• brainly.com/question/14283213?referrer=searchResults

I hope it helps you!