A distracted driver of a car of mass 1400 kg moving at a speed 20 m/s rear ends

Question

A distracted driver of a car of mass 1400 kg moving at a speed 20 m/s rear ends a truck of mass 2100 kg moving at a lower speed 13.7 m/s. After the collision, their bumpers lock. (

a) What is the speed of the vehicles after the collision?

(b) How much energy was lost in the collision? [Note: Depending on the numbers that you are given for this problem, you may need to use many digits of precision in the final speed as possible. Because there is a difference between two large numbers, if they are close enough, you'll need extra precision to get the 1% accuracy that WebAssign uses as a test.]

Explanation / Answer

here ,

a) let the speed of the vehicles is v

using conservation of momentum

(1400 + 2100 ) * v = 2100 * 13.7 + 1400 * 20

solving for v

v = 16.22 m/s

the speed of the vehicles after the collision is 16.22 m/s

b) for the loss in kinetic energy

loss in kientic energy = initial kienic energy - final kinetic energy

loss in kientic energy = 0.50 * 2100 * 13.7^2 + 0.50 * 1400 * 20^2 - 0.50 * (1400 + 2100 )* 16.22^2

loss in kientic energy = 16670 J

the loss in kientic energy is 16670 J

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