Question

A 925 kg car travelling on an icy road at a velocity of 18.0 m/s in a positive direction collides with a stationary truck with an unknown mass. If the two vehicles lock together upon collision and move with a combined velocity of 7.00 m/s, what is the mass of the truck?

Answer 1

The mass of the truck involved in a collision with a car, determined through the conservation of momentum, is found to be 2143 kg.

Step-by-step explanation:

To determine the mass of the truck after a collision with a car on an icy road, we can use the principle of conservation of momentum, according to which the total momentum of a system is conserved in the absence of external forces. In this case, the car with a mass of 925 kg and initial velocity of 18.0 m/s collides with a stationary truck, and after the collision, they move together with a velocity of 7.00 m/s.

Let mtruck be the mass of the truck. The initial momentum of the system is the momentum of the car, pi = mcar × vcar, which is 925 kg × 18.0 m/s. The final momentum of the system is the combined momentum of the car and truck, pf = (mcar + mtruck) × vcombined, which is (925 kg + mtruck) × 7.00 m/s.

Setting the initial momentum equal to the final momentum gives us the equation:
925 kg × 18.0 m/s = (925 kg + mtruck) × 7.00 m/s.

Solving for mtruck, we find that the mass of the truck is 2143 kg.