Question

A 3,000 kg car moving at 50 m/s due east collides with a 5,000 kg suv moving at 40 m/s due west. Calculate the total momentum of both vehicles

Answer 1

Given,

The mass of the car that is moving due east, m₁=3000 kg

The speed of the car that is moving due east, v₁=50 m/s

The mass of the car that is moving due west, m₂=5000 kg

The mass of the car that is moving due west, v₂=-40 m/s

Here we consider the east as the positive direction and the west as the negative direction. That is why the velocity of the car moving west is a negative quantity.

The momentum of an object is the product of the mass and the velocity of the object.

Thus the total momentum of the two objects is given by,

$P=m_1v_1+m_2v_2$

On substituting the known values,

$\begin{gathered} P=3000\times50+5000\times-40 \\ =-50000\text{ kg}\cdot\text{m/s} \end{gathered}$

Therefore the total momentum of both vehicles is -50000 kg·m/s

The negative sign indicates that the momentum vector is directed westwards.