A tennis player places a 63 kg ball machine on a frictionless surface the machine fires a 0.057 kg tennis ball horizontally with a velocity of 43 m/s toward the north what is the final velocity of the machine
To determine the final velocity of the machine, we can apply the principle of conservation of momentum.
According to the principle, the total momentum before the interaction is equal to the total momentum after the interaction.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Before the interaction, the momentum of the machine can be calculated as:
Machine momentum = machine mass × machine initial velocity
Given that the mass of the machine is 63 kg and the initial velocity of the machine is 0 m/s (since the question does not provide the initial velocity), the machine momentum is 0 kg*m/s.
The momentum of the tennis ball before the interaction is:
Tennis ball momentum = tennis ball mass × tennis ball initial velocity
= 0.057 kg × 43 m/s
= 2.451 kg*m/s
After the interaction, the momentum of the machine and the tennis ball combined should be zero since they are on a frictionless surface and no external forces are acting on the system.
Therefore, the momentum of the machine after the interaction should be equal to minus the momentum of the tennis ball before the interaction.
Machine momentum = - Tennis ball momentum
0 kg*m/s = -2.451 kg*m/s
Thus, the final velocity of the machine would be 0 m/s since its momentum is zero.