A cart is coasting at a speed v A 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 stops. However, if this same amount of mass is thrown out the back of the wagon, at the
same relative speed as before, the wagon accelerates to a new speed v B . Calculate the ratio v B /v A .

conservation of momentum

a) mVa=.9m*0+.1m*'v

throwing speed=mVa/.1m=10Va

b) mVa=.9m*Vb-.1m(10Va)
calculate Vb/Va

20/9

To calculate the ratio of vB/vA, we need to understand the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant unless acted upon by an external force.

In this scenario, when ten percent of the wagon's mass is thrown off parallel to the ground and in the forward direction, it causes the wagon to stop. This means that the momentum of the system before the mass is thrown off is equal to zero.

When the mass is thrown out the back of the wagon at the same relative speed as before, the wagon accelerates to a new speed vB. In this case, the momentum of the system will not be zero, as the mass is thrown in the opposite direction to the original motion.

Let's denote the mass of the wagon as M and the mass thrown out as m (10% of M). The initial momentum is zero, and the final momentum is given by the product of the wagon's mass and velocity (M * vB).

Using the principle of conservation of momentum, we can write:

Initial Momentum = Final Momentum

0 = M * vA - m * vA = (M - m) * vA

Simplifying the equation, we have:

M * vA = m * vA + (M - m) * vB

Since we know that m = 0.1M (as it is 10% of M), we can substitute it in the equation:

M * vA = 0.1M * vA + (M - 0.1M) * vB
M * vA = 0.1M * vA + 0.9M * vB
vA = 0.1vA + 0.9vB
0.9vB = 0.9vA
vB = vA

Therefore, the ratio vB/vA is equal to 1.