Question

<1>

An automobile of mass 1500kg moving at 25m/s collides with a truck of mass 4500kg at rest. This time, the car and the truck bounce off each other completely elastically. What is the final velocity of the truck after the collision? Call the direction of the automobile before the collision positive.

<2>

An automobile of mass 1500kg moving at 25m/s collides with a truck of mass 4500kg at rest. This time, the car and the truck bounce off each other completely elastically. What is the final velocity of the car after the collision? Call the initial direction of the automobile positive.

Answer 1

The initial direction of the velocity of the automobile before the collision is positive.

Mass of the automobile = m₁ = 1500 kg

Mass of the truck = m₂ = 4500 kg

Velocity of the automobile before the collision = V₁ = 25 m/s

Velocity of the truck before the collision = V₂ = 0 m/s (At rest)

Velocity of the automobile after the collision = V₃

Velocity of the truck after the collision = V₄

The collision is completely elastic.

Coefficient of restitution = e = 1

V₄ = V₃ + 25

By conservation of linear momentum,

m₁V₁ + m₂V₂ = m₁V₃ + m₂V₄

(1500)(25) + (4500)(0) = (1500)V₃ + (4500)(V₃ + 25)

37500 = 1500V₃ + 4500V₃ + 112500

6000V₃ = -75000

V₃ = -12.5 m/s

Negative sign indicates it is moving in the opposite direction of the initial direction of the automobile.

V₄ = V₃ + 25

V₄ = (-12.5) + 25

V₄ = 12.5 m/s

1) Final velocity of the truck after the collision = 12.5 m/s

2) Final velocity of the car after the collision = -12.5 m/s