Question

A car of mass 1000kg heading up the M1 at 50m/s collides with a stationary truck of mass 8000kg and sticks to it. What velocity does the wreckage move forward at?

A) 6.25 m/s
B) 5 m/s
C) 45 m/s
D) 40 m/s

Answer 1

Using conservation of momentum, the wreckage of a car and truck collision will move forward at a velocity of approximately 5.56 m/s, which is closest to option (B) 5 m/s.

Step-by-step explanation:

The question involves calculating the velocity of combined wreckage after a perfectly inelastic collision, using conservation of momentum. To solve for the velocity of the wreckage, we use the formula:

Conservation of Momentum: m1v1 + m2v2 = (m1 + m2)vw

Where m1 and v1 are the mass and velocity of the car, m2 and v2 are the mass and velocity of the truck (in this case 0 since the truck is stationary), and vw is the velocity of the wreckage.

Inserting the given values:

• m1 = 1000 kg (mass of the car)
• v1 = 50 m/s (velocity of the car)
• m2 = 8000 kg (mass of the truck)
• v2 = 0 m/s (velocity of the truck, since it is stationary)

Following the conservation of momentum, we calculate:

1000 kg * 50 m/s + 8000 kg * 0 m/s = (1000 kg + 8000 kg) * vw

Solving for vw gives:

vw = (1000 kg * 50 m/s) / (9000 kg) = 50000 kg*m/s / 9000 kg = 5.56 m/s

However, this calculated value is not exactly one of the multiple choice answers; there appears to be a calculation error. The correct calculation should yield:

vw = (1000 kg * 50 m/s) / (9000 kg) = 50000 kg*m/s / 9000 kg = 5.56 m/s (approximately 5.6 m/s, which is not in the provided choices)

The answer closest to this value from the available options is (B) 5 m/s.