An auto weighing 4000 lbs. and traveling at a velocity of 75 mph collides head o

Question

An auto weighing 4000 lbs. and traveling at a velocity of 75 mph collides head on with a smaller auto weighing 2500 lbs. and traveling 60 mph. When the autos collide. The autos lock together. Find the resultant velocity (speed and direction) of the two after impact. A machine gun fires 500 bullets/minute. If each bullet has mass of 30 grams and a muzzle velocity of 50 times 10^2 cm/s, find the average reaction of the gun on its support. If the autos in problem 1 had collided at an intersection (at an angle of 90 degrees), find the resultant velocity (speed and direction).

Explanation / Answer

mass of bigger auto = 4000 lbs or 1814.369 kg

mass of smaller auto = 2500 lbs or 1133.981 kg

velocity of bigger auto = 75 mph or 33.528 m/s

velocity of smaller auto = 60 mph or 26.822 m/s

by conservation of momentum

initial momentum = final momentum

1814.369 * 33.528 - 1133.981 * 26.822 = (1814.369 + 1133.981) * v

v = 10.316 m/s

resultant velocity = 10.316 m/s

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