Question

A car with a mass of 1.5 × 103 kilograms is traveling west at a velocity of 22 meters/second. It hits a stationary car with a mass of 9.0 × 102 kilograms. If the collision is inelastic, what is the final direction and approximate velocity of the two cars?

A. 14 meters/second to the west
B. 14 meters/second to the east
C. 22 meters/second to the east
D. 22 meters/second to the west

Answer 1

A. 14 meters/second to the west

Answer 2

A. 14 meters/second to the west

Step-by-step explanation:

The collision is inelastic, which means that:

- only the total momentum is conserved (not the kinetic energy)

- the two cars stick to each other and continue their motion together after the collision

Therefore, we can write the law of conservation of momentum as follows:

`m_1 u_1 + m_2 u_2 = (m_1 + m_2 )v`

where:

`m_1 = 1.5 \cdot 10^3 kg` is the mass of the first car

`u_1 = +22 m/s` is the initial velocity of the first car (let's take as positive the west direction)

`m_2 = 9.0 \cdot 10^2 kg` is the mass of the second car

`u_2 = 0` is the initial velocity of the second car

`v` is the final velocity of the two cars

Re-arranging the equation, we get:

`v=(m_1 u_1)/(m_1 +m_2)=((1.5\cdot 10^3 kg)(+22 m/s))/(1.5\cdot 10^3 kg+9.0\cdot 10^2 kg)=+13.8 m/s`

So, approximately 14 m/s, and the direction is still west since the sign is positive.