Question

A baggage cart full of luggage is coasting at a speed v_A across the airport taxiway. When forty-one percent of the mass of the cart and luggage is thrown off the cart, parallel to the ground and in the forward direction, the cart is brought to a halt. If the direction in which this mass is thrown is exactly reversed, but the speed of this mass relative to the cart remains the same, the cart accelerates to a new speed v_B. Calculate the ratio v_B/v_A

Answer 1

"but the speed of this mass relative to the cart remains the same"
Let v be the velocity of the mass thrown off of the cart with respect to the cart.
Momentum with respect to the ground is conserved for both scenarios.

Thrown forward:

m(vA) = (0.41m)(v - vA)

vA = (41/100)v - (41/100)(vA)

(141/100)(vA) = (41/100)v

v = (141/41)(vA)

Thrown backward:

m(vA) = (0.41m)(-v - vA) + (0.59m)(vB)

(vA) = -(41/100)v - (41/100)(vA) + (59/100)(vB)

(141/100)(vA) = -(41/100)(141/41)(vA) + (59/100)(vB)

(141/50)(vA) = (59/100)(vB)

(vB)/(vA) = 282 / 59