Question

Bill and Ted are wearing Velcro suits and are running towardseach other. Bill has a mass of 60 kg and is running to the rightat 4 m/s; Ted has a mass of 50 kg and is running to the left at4.8 m/s. When they collide, they stick together (because yaknow, Velcro). Calculate their velocity after colliding witheach other.

Answer 1

We know that in a collision the momentum is conserved, that is:

`p_i=p_f`

where the momentum is given by:

`p=mv`

In this case the conservation of momentum can be express as:

`m_1v_1+m_2v_2=(m_1+m_2)u`

where m1 and m2 are the masses of the boys, v1 and v2 are their initial velocities and u is the final velocity after the collision. In this case we know that:

Bill mass is 60 kg and the initial velocity is 4 m/s.

Ted mass is 50 kg and the initial velocity is -4.8 m/s (the minus sign comes from the fact that he runs to the left).

Plugging these values and solving for u we have:

`\begin{gathered} (60)(4)+(50)(-4.8)=(60+50)u \\ u=((60)(4)+(50)(-4.8))/(60+50) \\ u=(240-240)/(110) \\ u=(0)/(110) \\ u=0 \end{gathered}`

Therefore, the velocity after they collide is zero. This means that after they collide, they stopped.