An SUV (mass: 1580kg) and a sports car (mass: 1225kg) are driving in opposite la

ID: 2115245 • Letter: A

Question

An SUV (mass: 1580kg) and a sports car (mass: 1225kg) are driving in opposite lanes in a

rural road. Unfortunately both of them are too close to the line and when they meet, they have a

glancing collision. A police car that is observing the collision measures the initial and the final

velocity of the sports car to be (0,40) m/s and (64.5, -24.5) m/s respectively. By observing the

trajectory of the SUV after the collision, he infers that its final velocity is (-50, -10) m/s.

Determine: a) What is the initial velocity of the SUV?. Remember that velocity is a vector; b)

Whether the collision elastic or inelastic. Explain your answer giving quantitative arguments.

(a) By conservation of momentum in the x-axis

we have

1580 x u1x + 1225 x 0 = 1580 x -50 + 1225 x 64.5

ie u1x = 0 m/sec

Similarly in Y-axis

1580 x u1y + 1225 x 40 = 1580 x -10 + 1225 x -24.5

ie u1y = -0.93 m/sec

Therefore, initial velocitu of SUV = (0,-0.93)

(b) Change in KE is not Zero

So, the collision is inelastic

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