Question

Two cars collide and stick together in the collision. Just before the collision, one car (mass = 1400 kg) was moving with a velocity of 10 m/s, and the other car (mass = 950 kg) was moving with a velocity of -12 m/s. Just after the collision, what is the velocity of the cars (which are now stuck together)?

A) -4.5 m/s
B) -2 m/s
C) -5.5 m/s
D) -3 m/s

Answer 1

Using the conservation of momentum for a perfectly inelastic collision, the final velocity of the cars stuck together after the collision is approximately 1.106 m/s in the original direction of the first car.

Step-by-step explanation:

The question involves a collision where two cars stick together after the impact. This is an example of a perfectly inelastic collision where the conservation of momentum applies. The momentum before the collision equals the momentum after the collision. The equation for momentum is p=mv, where p is momentum, m is mass, and v is velocity.

To calculate the final velocity of both cars after the collision, we use the formula:

(m1 * v1) + (m2 * v2) = (m1 + m2) * vfinal

Plugging in the given values:

(1400 kg * 10 m/s) + (950 kg * -12 m/s) = (1400 kg + 950 kg) * vfinal

14000 kg*m/s - 11400 kg*m/s = 2350 kg * vfinal

2600 kg*m/s = 2350 kg * vfinal

vfinal = 2600 kg*m/s ÷ 2350 kg = 1.106 m/s

Therefore, the final velocity of the cars stuck together just after the collision is approximately 1.106 m/s in the direction of the first car's original motion.