A wagon is coasting at a speed, vA, along a straight and level road. When ten percent of the wagon's mass is thrown off the wagon, parallel to the ground and in the forward direction, the wagon 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 wagon remains the same, the wagon accelerates to a new speed, vB. Calculate the ratio of vB/vA.

Question

A wagon is coasting at a speed, vA, along a straight and level road.  When ten percent of the wagon's mass is thrown off the wagon, parallel to the ground and in the forward direction, the wagon 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  wagon remains the same, the wagon accelerates to a new speed, vB.  Calculate the ratio of vB/vA.

shiv · Accepted Answer

Damon is absolutely right!

Damon · Answer

m and .1 m

original momentum
= m VA

momentum remains m Va throiughout
so
m Va = .1 m (Va+V)
and
m Va = .1 m (Va-V) + .9 m Vb
so
.1 m Va+.1 m V = .1 m Va-.1 m V+.9 m Vb
.2 m V = .9 m Vb
so
V = 4.5 Vb
but
m Va = .1 m Va + .1 m V
so
V = 9 Va
so
9 Va = 4.5 Vb
Vb/Va = 2

David · Answer

No, youa are wrong. It is not mVa = .1m(Va-V) + .9mVb it is mVa = (-).1m(Va+V) + .9mVb it is not 2, it is 20/9