A railroad handcar is moving along straight, frictionless tracks with negligible

Question

A railroad handcar is moving along straight, frictionless tracks with negligible air resistance. In the following cases, the car initially has a total mass (car and contents) of 170 kg and is traveling east with a velocity of magnitude 5.00 m/s . Find the final velocity of the car in each case, assuming that the handcar does not leave the tracks.

a. An object with a mass of 30.0 kg is thrown sideways out of the car with a speed of 1.50 m/srelative to the car's initial velocity.

b. An object with a mass of 30.0 kg is thrown backward out of the car with a velocity of 5.00 m/srelative to the initial motion of the car

c.An object with a mass of 30.0 kg is thrown into the car with a velocity of 6.30 m/s relative to the ground and opposite in direction to the initial velocity of the car.

Explanation / Answer

a) Applying momentum conservation,

assume car direction is along i vector and sidways direction as j .

170 x 5i = 140 x v + 30 x 1.50j

v = 6.07i   - 0.053j m/s

speed = sqrt(6.07^2 + 0.053^2 ) = 6.07 m/s

b) using moementum conservation,

170 x 5    = 140 x v - 30 x 6.30

v = 7.42 m/s

c) using momentum conservation,

170 x 5   - 30 x 6.30 = (170 + 30)v

v =3.31 m/s

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