During hand-pumped rail car races, a speed of 31 km/h has been achieved by teams

Question

During hand-pumped rail car races, a speed of 31 km/h has been achieved by teams of four people. The car of mass 337 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 20.6 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

let the velocity of car after jumped by man is v

v0-v = -4

v= vo+4

apply conservation of linear momentum

(mc+ 4 mp ) 31 km/h( 1000 m/3600 s) = mc v = 4 mp ( v-4)

( 337 +4 * 75)8.61 m/s = 337 v +300(v-4)

6684.57 = 637 v

v = 10.49 m/s

(a)

time = d/ horizontal velocity = 20.6/10.49 = 1.96 s

(b)

horizontal vlocity of the pumpers when thy hit the ground is

vp = vc - up = 10.49 m/s -4.0 m/s = 6.49 m/s

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