A tennis player places a 55 kg ball machine on a frictionless surface. The machine fires a 0.065 kg tennis ball horizontally with a velocity of 55 m/s toward the north. What is the final velocity of the machine?
Enter your answer here: m/s
its the negative of the .065
To find the final velocity of the machine, we can use the law of conservation of momentum. The initial momentum of the system consisting of the ball and the machine is equal to the final momentum of the system.
The initial momentum before the ball is fired is given by:
Initial momentum = Mass of the ball x Initial velocity of the ball
Let's calculate the initial momentum:
Initial momentum = 0.065 kg x 55 m/s (since the mass of the ball is 0.065 kg and the initial velocity is 55 m/s)
Initial momentum = 3.575 kg.m/s
Since the ball is the only object in the system that moves horizontally, the horizontal component of the momentum after the ball is fired is equal to the horizontal component of the momentum before the ball is fired.
The final momentum after the ball is fired is given by:
Final momentum = Mass of the machine x Final velocity of the machine
Let's calculate the final momentum:
Final momentum = 55 kg x Final velocity of the machine (since the mass of the machine is 55 kg)
Now, equating the initial and final momentum:
Initial momentum = Final momentum
3.575 kg.m/s = 55 kg x Final velocity of the machine
Dividing both sides of the equation by 55 kg:
Final velocity of the machine = 3.575 kg.m/s / 55 kg
Final velocity of the machine ≈ 0.065 m/s
Therefore, the final velocity of the machine is approximately 0.065 m/s.
To find the final velocity of the machine, we will use the principle of conservation of momentum. This principle states that the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
In this case, the ball machine and the tennis ball are the system. Before the firing of the ball, the machine is at rest, so its initial momentum is zero. The momentum of the tennis ball, on the other hand, can be calculated using the equation:
momentum = mass x velocity
The momentum of the tennis ball is given by:
momentum = 0.065 kg x 55 m/s
Now, after the ball is fired, both the machine and the tennis ball will move together. Let's assume that the final velocity of the machine is Vf. The momentum of the combined system (machine + ball) after the firing is given by:
momentum = (mass of machine + mass of ball) x Vf
Using the equation for conservation of momentum, we can equate the two momenta:
0.065 kg x 55 m/s = (55 kg + 0.065 kg) x Vf
Now, we can solve for Vf:
Vf = (0.065 kg x 55 m/s) / (55 kg + 0.065 kg)
Calculating this expression will give us the final velocity of the machine.