A tennis player places a 51 kg ball machine on a frictionless surface, as shown below. The machine fires a 0.067 kg tennis ball horizontally with a velocity of 33.4 m/s toward the north. What is the final velocity of the machine?
Can you please EXPLAIN how to get the answer?!
Check answers to "related questions" below. Your numbers have changed a little. The method of solution is the same.
To determine the final velocity of the machine, we can use the concept of conservation of momentum.
Conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system. In this case, the system consists of the ball machine and the tennis ball.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = m * v
Before the ball is fired, both the ball machine and the tennis ball are at rest. This means the initial momentum of the system is zero.
After the ball is fired, the tennis ball moves with a velocity of 33.4 m/s towards the north. Let's assume the final velocity of the ball machine is v_m.
Using conservation of momentum, we can set up the equation:
Initial momentum = Final momentum
(0 kg * 0 m/s) + (51 kg * 0 m/s) = (0.067 kg * 33.4 m/s) + (51 kg * v_m)
Simplifying the equation:
0 = 2.2388 kg·m/s + 51 kg · v_m
Now, we can solve for v_m:
51 kg · v_m = -2.2388 kg·m/s
v_m = -2.2388 kg·m/s / 51 kg
v_m ≈ -0.0439 m/s
Therefore, the final velocity of the machine is approximately -0.0439 m/s towards the north.
Note: The negative sign indicates that the machine moves in the opposite direction to the tennis ball.