Ans A) 10ft/s b) 11.1 c) 8 A railroad car is coasting along straight frictionles

Question

Ans A) 10ft/s b) 11.1 c) 8 A railroad car is coasting along straight frictionless tracks. In each part of the problem, the car (and contents) initially weigh 500 lbs, and the car is traveling 10.0 ft/s in the X direction. Find the final velocity of the car, if a 50 lb weight is thrown sideways (Y-direction) out of the car with a velocity 8.0 ft/s relative to the car. a 50 lb weight is thrown backward out of the car with a velocity 10.0 ft/s relative to the car's initial velocity. a 50 lb weight is thrown into the car with a velocity 12.0 ft/s relative to the ground and in direction opposite to the velocity of the car.

Explanation / Answer

here,

velocity of car, vc = 10 ft/s
mass of car, mc = 500 lbs

mass of stone, ms = 50 lb
Velocity of stone, Vs

From Conservation of momentum,
mc*vc + 0 = mc*vc' + ms*vs

where,
vc' = final velocity of car
vs is velocity of stone

rewriting above eqn for final velocity of car, vc'

vc' = (mc*vc - ms*vs)/mc ------------------(1)
(above equation only valid for x axis motion.)

Part A:
Since stone has been thrown in y direction, but there is no momentum in x dirction so, car velocity will remain same
Vc' = mc*vc/mc ( Vs = 0 in x direction)
Vc' = vc
vc = 10 ft/s

Part B:
vs = -10 ft/s, from equaiton 1 we have

vc' = (500*10 + 50*10)/500
Vc' = 11 ft/s

Part C:
vs = 12 ft/s, from equaiton 1 we have

vc' = (500*10 - 50*12)/500
Vc' = 8 ft/s

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