A vehicle with mass of 950 kg is driving east with a velocity of12.0 m/s. It cra

Question

A vehicle with mass of 950 kg is driving east with a velocity of12.0 m/s. It crashes into a stationary vehicle of the samemass. Assume an elastic collision. The first vehicle is deflectedat an angle of 40 degrees north of its original path. The secondvehicle's path is 90 degrees to the right of the first vehicle'sfinal path.

a) What is the momentum of the first vehicle after the crash?
b) what is the momentum of the 2nd vehicle after the crash?
c) What is the velocity of the 1st vehicle after the crash?
d) What is velocity of the 2nd vehicle after the crash?

Explanation / Answer

mass m = 950 kg Initial speed of 1 st vehicle u = 12 m / s Initial velocity of 2 nd vehicle U - 0 m /s In east direction : ----------------- from law of conservation of momentum , m u + m U = m v cos 40 + M V cos 50              12 = 0.7666 v + 0.642V              ---------------( 1) In north direction : ----------------- apply law of conservation of momentum ,     0 = m v sin 40 - m V sin 50   v sin 40 = V sin 50            V= 0.839 v     ----------( 2) substitue eq ( 2 ) in eq ( 1 ) we get 12 = 0.7666 v + 0.642 * 0.839 v from this v = 9.1932 m / s So, V = 0.839 v = 7.173 m / s (a). the momentum of the first vehicle after the crash = mv                                                                               = 8733.54 kg m / s
b) the momentum of the 2nd vehicle after the crash = m V                                                                            = 6814.35 kg m / s
c) the velocity of the 1st vehicle after the crash = 9.1932 m /s
d) velocity of the 2nd vehicle after the crash = 7.173 m / s

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