During hand-pumped rail car races, a speed of 27 km/h has been achieved by teams

Question

During hand-pumped rail car races, a speed of 27 km/h has been achieved by teams of four people. The car of mass 347 kg (when measured without people on it) is moving at that speed toward a river when Carlos, the chief pumper, notices that the bridge ahead is out. All four people (each with a mass of 75.0 kg) simultaneously jump backward off the car with a velocity that has a magnitude of 4.00 m/s relative to the new velocity of the car. The car then runs off the bank and falls into the water a horizontal distance of 26 m from the bank.

(a) How long is the time of fall of the rail car?

(b) What is the horizontal component of the velocity of the pumpers when they hit the ground?

Explanation / Answer

given,

mass of car = 347 kg

initial speed = 27 km/h or 7.5 m/s

mass of each pumpers = 75 kg

by conservation of momentum

initial momentum = final momentum

(347 + 4 * 75) * 7.5 = 347 * v - 4 * 75 * (v - 4)

v = 77.7128 m/s

time = distance / speed

time = 26 / 77.7128

time of fall of the rail car = 0.334 sec

horizontal component of the velocity of the pumpers when they hit the ground = 77.7128 - 4

horizontal component of the velocity of the pumpers when they hit the ground = 73.7128 m/s

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