Question

12.A 48.0 kg woman, riding on a 12 kg cart, is moving east at 8.0 m/s. The

Answer 1

The final velocity of the cart is 20.0 m/s eastward

Explanation:

If there are no external forces acting on the system, the total momentum of the woman+cart system must be conserved. Therefore, we can write:

$p_i = p_f\\(m+M)u = mv+MV$

where:

m = 12 kg is the mass of the cart

M = 48 kg is the mass of the woman

u = 8.0 m/s is the initial velocity of the woman and the cart (they move together). We take east as positive direction

V = 5.0 m/s is the final velocity of the woman

v is the final velocity of the cart

Solving for v, we find:

$v=\frac{(m+M)v-MV}{m}=\frac{(12+48)(8.0)-(48)(5.0)}{12}=20 m/s$

And the positive sign indicates that the direction is eastward.

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