Question

A 60 kg boy and 40 kg girl stand on skateboards on a frictionless, horizontal surface. The boy pushes the girl away from him. The girl gains a speed of 0.3 m/s during the 0.50 s the boy's hands are in contact with her.

1. What will be the boy's speed after?
2. Assuming that in each case the girl achieved the same speed, would it matter whether the boy pushed the girl, the girl pushed the boy, or they put their hands together and pushed each other away?

Answer 1

According to the law of conservation of linear momentum, the sum of intial andfinal momentum of a sytem is zero if there is no external force present.

Intially, the boy and girl are at rest. So, p_i is zero.

After the boy pushes the girl away, the momentum of the girl becomes p_g= 40*0.3 =12Kgm/s

Now according to the law of conservation of linear momentum,

_Pi=p_f

p_i=0 and p_f=p_b+p_g

0=p_b+p_g

p_b=-p_g

m_b*v_b=-12

60*v_b=-12

v_b=-0.2m/s

So, the speed with which the boy goes is 0.2m/s.The negative sign is just for the reverse direction as from the girl.

It won't matter who pushes whom, if the girl gets the same speed of 0.3m/s then the boy gets the speed of 0.2m/s.