Question

A motorcyclist has a mass of 300 kg and is travelling down a road when he collides into the back of a stationary school bus with a mass of 1,500 kg. After the collision the motorcyclist bounces backwards with a velocity of 7.56 m/s. The bus is pushed forwards with a velocity of 7.05 m/s. If the speed limit on the street was 10 m/s, should the motorcyclist be held guilty for speeding?

Answer 1

Given that the mass of the bike is m = 300 kg

The mass of the bus is M = 1500 kg

The initial velocity of the bus is u_M = 0 m/s

The final velocity of the bus is v_M = 7.05 m/s

The final velocity of the bike is v_m = 7.56 m/s

Let the initial velocity of the bike be u_m.

According to the conservation of momentum,

$mu_m+Mu_M=-mv_m+Mv_M$

Substituting the values, the initial velocity of the bike will be

$\begin{gathered} 300u_m+1500\times0=-300\times7.56+1500\times7.05_{} \\ u_m=\frac{8307}{300} \\ =27.69\text{ m/s} \end{gathered}$

As the initial velocity of the bike is more than 10 m/s, the motorcyclist should be held guilty for speeding.