A tennis player places a 44 kg ball machine on a frictionless surface, as shown below. The machine fires a 0.064 kg tennis ball horizontally with a velocity of 35.2 m/s toward the north. What is the final velocity of the machine?
.0512 m/s south
Well, if the machine is firing tennis balls towards the north, then it's probably trying to escape the tennis court and join the circus. So, the final velocity of the machine would be its escape velocity, which can only be achieved by turning on its clown shoes and running away as fast as it can! So, put on your clown wig and join the machine as it flees the tennis court with a final velocity of "as fast as possible"!
To find the final velocity of the machine, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, assuming no external forces are acting.
In this case, the initial momentum of the ball machine is zero since it’s at rest. The momentum of the fired tennis ball can be calculated by multiplying its mass and velocity:
Initial momentum of the ball machine (before firing) = 0 kg.m/s
Momentum of the tennis ball (before firing) = 0.064 kg × 35.2 m/s (toward the north)
Now, since no external forces are acting on the system, and the mass of the ball machine is much larger than the mass of the tennis ball, the final velocity of the ball machine after firing will be in the opposite direction with a magnitude that can be found using the principle of conservation of momentum:
Initial momentum = Final momentum
0 = (0.064 kg × 35.2 m/s) + (final velocity of the machine × 44 kg)
Solving the equation for the final velocity of the machine:
0 = (0.064 kg × 35.2 m/s) + (final velocity of the machine × 44 kg)
-(0.064 kg × 35.2 m/s) = final velocity of the machine × 44 kg
final velocity of the machine = -(0.064 kg × 35.2 m/s) / 44 kg
Evaluating the expression:
final velocity of the machine = - 0.05056 m/s
Therefore, the final velocity of the machine is approximately -0.05056 m/s toward the south. The negative sign indicates that the machine moves in the opposite direction to the fired tennis ball.
m1 * v1 = m2 * v2
44v = .064*35.2