Question

A 45.0-kg girl stands on a 13.0-kg wagon holding two 18.0-kg weights. She throws the weights horizontally off the back of the wagon at a speed of 6.5 m/s relative to herself . Assuming that the wagon was at rest initially, what is the speed of the girl relative to the ground after she throws both weights at the same time

Answer 1

v = 4.0 m/s

Step-by-step explanation:

• Assuming no external forces acting during the instant that the girl throws the weights, total momentum must be conserved.
• Since all the masses at rest initially, the initial momentum must be zero.
• So, due to momentum must keep constant, final momentum must be zero too, as follows:

`p_(f) = m_(w) * v_(w) + m_(g+w) *v_(g+w) = 0 (1)`

• Assuming the direction towards the back of the wagon as positive, and replacing the masses in (1), we can solve for vg, as follows:

`v_(g+w) =- (m_(w) *v_(w))/(m_(g+w) ) = - (36.0kg *6.5m/s)/(58.0kg ) = -4.0m/s (2)`

• This means that the girl (along with the wagon on she is standing) will move at a speed of 4.0 m/s in an opposite direction to the one she threw the weights.