During hand-pumped rail car races, a speed of 32.4 km/h has been achieved by tea

Question

During hand-pumped rail car races, a speed of 32.4 km/h has been achieved by teams of four people. The car of mass 398 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 22.8 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

According to conservation of momentum

m1 u1 + m2 ( u1 - 4 ) = 0

m1 is the mass of the car and m2 is the mass of the people

398 u1 + 4(75) (u1 - 4 ) = 0

solving for u1 = 1.72m/s

The relative speed of the car to the speed of the center of mass is

V = 1.72 + (32.4 )(5/18 ) = 10.72 m/s

The time of fall is

t = 22.4 / 10.72 = 2.09s

b)

the horizontal component of the velocity of the pumpers when they hit the ground is

Vp = 10.72 m/s - 4 m/s = 6.72 m/s

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