A 750 kg car is stalled on an icy road during a snowstorm. A 1000 kg car traveli

Question

A 750 kg car is stalled on an icy road during a snowstorm. A 1000 kg car traveling eastbound at 15 m/s collides with the rear of the stalled car. After being hit, the 750 kg car slides on the ice at 4 m/s in a direction 30 north of east.

Part A

What is the magnitude of the velocity of the 1000 kg car after the collision?

Express your answer in meters per seconds to two significant figures.

Part B

What is the direction of the velocity of the 1000 kg car after the collision?

Express your answer in degrees to two significant figures.

Part C

Calculate the ratio of the kinetic energy of the two cars just after the collision to that just before the collision. (You may ignore the effects of friction during the collision.)

Express your answer to two significant figures.

Explanation / Answer

LEt east be denoted by i, north be denoted by j
M = 1000
m = 750
Initial momentum = 1000*15 i = 15000i
Final momentum about x = 750*4cos(30) + 1000*vcos(theta)
Final momentum about y = 750*4sin(30) + 1000vsin(theta)
by conservation of momentum
vsin(theta) = -1.5
3000*cos(30) + 1000*(-1.5cos(theta)/sin(theta)) = 15000
theta = -6.8963 deg
1. v = 12.492 m/s
2. theta = -12.492 deg

so v = 12.492[cos(-6.8963) i + sin(-6.8963) j]
3. 0.5(750*4^2+1000*12.492^2)/0.5*1000*15^2 = 0.74688

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