A boy throws a 4-kg pumpkin at 8 m/s to a 40-kg girl on roller skates, who catches it. At what speed does the girl then move backward?
you have to use conservation of momentum, and conservation of energy on this. Remember the boy moves after he throws it also.
I don't understand how to work it?
To find the speed at which the girl moves backward after catching the pumpkin, we need to use the principle of conservation of momentum. According to this principle, the total initial momentum of the system should be equal to the total final momentum.
The initial momentum of the pumpkin is given by the formula:
Initial momentum of the pumpkin = mass of the pumpkin × initial velocity of the pumpkin
Given that the mass of the pumpkin is 4 kg and its initial velocity is 8 m/s:
Initial momentum of the pumpkin = 4 kg × 8 m/s = 32 kg·m/s
The initial momentum of the girl is zero since she is initially at rest.
Now, after the girl catches the pumpkin and starts moving backward, the final momentum of the system will also be zero since there are no external forces acting on the horizontal motion.
So, the final momentum of the system is zero, which means:
Final momentum of the system = Final momentum of the pumpkin + Final momentum of the girl = 0
Therefore, the momentum of the girl after catching the pumpkin must be equal in magnitude and opposite in direction to the momentum of the pumpkin before catching it.
Since the mass of the girl is 40 kg and the initial momentum of the pumpkin is 32 kg·m/s, the girl's velocity can be calculated as follows:
Final velocity of the girl = -(Initial momentum of the pumpkin)/(mass of the girl) = -32 kg·m/s / 40 kg
Final velocity of the girl = -0.8 m/s
Hence, the girl moves backward at a speed of 0.8 m/s.