Question

Let’s say I am in a bumper car and have a velocity of 14 m/s, driving in the positive x-direction. I and my bumped car have a mass of 120 kg. You are in a bumper car, sitting still. I run into you, and we collide elastically. I end up with a velocity of 2 m/s going in the negative x-direction. What is your mass, and what is your final velocity?

Answer 1

160 kg

12 m/s

Step-by-step explanation:

`m_1` = Mass of first car = 120 kg

`m_2` = Mass of second car

`u_1` = Initial Velocity of first car = 14 m/s

`u_2` = Initial Velocity of second car = 0 m/s

`v_1` = Final Velocity of first car = -2 m/s

`v_2` = Final Velocity of second car

For perfectly elastic collision

`m_(1)u_(1)+m_(2)u_(2)=m_(1)v_(1)+m_(2)v_(2)\\\Rightarrow m_2v_2=m_(1)u_(1)+m_(2)u_(2)-m_(1)v_(1)\\\Rightarrow m_2v_2=120* 14+m_2* 0-(120* -2)\\\Rightarrow m_2v_2=1920\\\Rightarrow m_2=(1920)/(v_2)`

Applying in the next equation

`v_2=(2m_1)/(m_1+m_2)u_(1)+(m_2-m_1)/(m_1+m_2)u_2\\\Rightarrow v_2=(2* 120)/(120+(1920)/(v_2))* 14+(m_2-m_1)/(m_1+m_2)* 0\\\Rightarrow \left(120+(1920)/(v_2)\right)v_2=3360\\\Rightarrow 120v_2+1920=3360\\\Rightarrow v_2=(3360-1920)/(120)\\\Rightarrow v_2=12\ m/s`

`m_2=(1920)/(v_2)\\\Rightarrow m_2=(1920)/(12)\\\Rightarrow m_2=160\ kg`

Mass of second car = 160 kg

Velocity of second car = 12 m/s