Question

A car traveling at 10 m/s slams into a trash can on the side of the road. The trash can

sticks to the front of the car and they move as one object. If the momentum is

conserved, what would happen to the velocity of the car after the collision?

The velocity would decrease

It would remain the same

The velocity would increase

The car comes to rest

Answer 1

Answer:

The velocity would decrease

Explanation:

Let

$m_1$ = Mass of car

$m_2$ = Mass of trash can

$u_1$ = Initial velocity of car = 10 m/s

$u_2$ = Initial velocity of trash can = 0

v = Velocity of combined mass

From the question the momentum balance of the system will be

$m_1u_1+m_2u_2=(m_1+m_2)v\\\Rightarrow v=\dfrac{m_1u_1+m_2u_2}{m_1+m_2}\\\Rightarrow v=\dfrac{10m_1}{m_1+m_2}$

The velocity would decrease as now the mass of the car and trash will both be moving as one. The mass would increase resulting in a lower velocity of the combined mass.