An empty train car of mass 2.0 x 104kg coasts along at 10 m/s. A 3000-kg boulder is suddenly dropped vertically into the car. Find the speed of the car immediately after the boulder is dropped in.

The speed of the car immediately after the boulder is dropped = 8.696 m/s

Explanation:

Newton's Third Law Of Motion: Its states that to every action there is an equal and opposite reaction.

From Newton's third law of motion,

The momentum of the empty train car before the boulder dropped = momentum of the train car after the boulder is dropped.

But Momentum = mass * Velocity.

m₁u₁ = m₂u₂ ... Equation 1

Making u₂ the subject of the equation,

u₂ = m₁u₁/m₂ ... Equation 2

Where m₁ = mass of the empty train car, m₂ = mass of the train car and the boulder, u₁ = velocity of the train car before the boulder is dropped, u₂ = velocity of the train car after the boulder is dropped.

Given: m₁ = 20000 kg, m₂ = 20000 + 3000 = 23000 kg, u₁ = 10 m/s.

Substituting these values into equation 2,

u₂ = (20000 * 10) / 23000

u₂ = 8.696 m/s

Therefore the speed of the car immediately after the boulder is dropped = 8.696 m/s