An automobile of mass 1500 kg moving at 25 m/s colides with a truck of mass 4500

Question

An automobile of mass 1500 kg moving at 25 m/s colides with a truck of mass 4500 kg at rest. This time, the car and the truck bounce aff each other completely elastically. What is the final velocity of the car after the collision? Call the initial direction of the automobile positive. An automobile of mass 1500 kg moving at 25 m/s colides with a truck of mass 4500 kg at rest. This time, the car and the truck bounce aff each other completely elastically. What is the final velocity of the truck after the collision? Call the direction of the automobile before the collision positive.

Explanation / Answer

we use conservation of momentum and energy conservation of momentum means momentum before equals momentum after call v1 the speed of the smaller car after collision and v2 the speed of the larger car we have 1500kgx25m/s = 1500v1+4500v2 this can be written v2=(37500-1500v1)/4500 energy conservation tells us 1/2 (1500)(25)^2=1/2(1500)v1^2 +1/2(4500)v2^2 into this equation, substitute v2=(37500-1500v1)/4500 this gives you a quadratic in v1, solve via quadratic equation to get that v1=-12.5m/s and v2=+12.5m/s

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