Question

Two remote control cars with masses of 1.13 kilograms and 1.94 kilograms travel toward each other at speeds of 8.50 meters per second and 3.79 meters per second, respectively. The cars collide head-on, and the less massive car recoils with a speed of 2.02 meters per second.What is the final speed of the second car? Include units in your answer. Must be in 3 significant digits.

Answer 1

Given data

Let the speed of the first car in the positive direction and the second car is in negative direction as it travels towards each other.

*The given mass of the first remote control car is m = 1.13 kg

*The initial speed of the first remote control car is u_1 = +8.50 m/s

*The given mass of the second remote control car is M = 1.94 kg

*The initial speed of the second remote control car is u_2 = -3.79 m/s

*The final speed of the first remote control car is v_1 = -2.02 m/s

The formula for the final velocity of the car is given by the conservation of momentum as

`mu_1+Mu_2=mv_1+Mv_2`

*Here v_2 is the final speed of the second car

Substitute the known values in the above expression as

`\begin{gathered} (1.13)(8.50)+(1.94)(-3.79)=(1.13)(-2.02)+(1.94)v_2 \\ 2.252=-2.282+1.94v_2 \\ v_2=2.33\text{ m/s} \end{gathered}`

Hence, the final speed of the second car is v_2 = +2.33 m/s