A 1094 kg van, stopped at a traffic light, is hit directly in the rear by...

A 1094 kg van, stopped at a traffic light, is hit directly in the rear by a 727 kg car traveling with a velocity of +2.41 m/s. Assume that the transmission of the van is in neutral, the brakes are not being applied, and the collision is elastic. What is the final velocity of the car?

Solutions

Expert Solution

From the law of conservation of momentum, we have

m2v2 + m1v1 = 0 + m1u1

1094*v2 + 727*v1 = 727*2.41

Rewrite the equation for v2.

v2 = [727*2.41-727*v1] / 1094 = 1.60 - (0.6645)v₁

From the law of conservation of energy, we have

1/2m1v1² + 1/2m2v2² = 0+ 1/2m2u2²

1094*v2^2 +727v1^2 = 727*2.41^2

1094*v2^2 +727v1^2 = 4222.4887

1094[1.60 - (0.6645)v₁]2 + 727v1^2 = 4222.4887

{1094[2.56 +(0.44156025)v₁²-(2.1264)v₁]} + 727v1^2 = 4222.4887

Write the equation in the form of quadratic equation:

(1208.0669135)v₁² - (2326.2816)v1 - 1421.8487= 0

Solutions: v1 = 2.41 m/s and -0.487 m/s. In this case, the car travel after collision along the negative x-axis.

So, the final velocity of the car is, -0.487 m/s.

Note:

Final velocity of the van is, v2 = 1.60 - (0.6645)v₁= 1.60 - 0.6645*-0.487 = 1.92 m/s

genius_generous answered 1 year ago

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