A tennis player places a 54 kg ball machine on a frictionless surface. The machine fires a 0.057 kg tennis ball horizontally with a velocity of 38 m/s toward the north. What is the final velocity of the machine?
m/s to the south
Total momentum remains zero. After the ball is thrown, ball momentum and machine momentum are equal and opposite.
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 the collision is equal to the total momentum after the collision.
Before the collision, the momentum of the tennis ball is calculated by multiplying its mass (0.057 kg) with its velocity (38 m/s). Since the ball is fired horizontally, the vertical component of its velocity does not contribute to its momentum.
Momentum of the ball = mass of the ball × velocity of the ball
= 0.057 kg × 38 m/s
= 2.166 kg·m/s
After the collision, the momentum of the tennis ball machine will be equal in magnitude but opposite in direction to cancel out the momentum of the tennis ball.
Given that the mass of the tennis ball machine is 54 kg, let's assume its final velocity is v_final.
Momentum of the machine = mass of the machine × velocity of the machine
= 54 kg × v_final
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
Momentum of the ball + Momentum of the machine = 0
2.166 kg·m/s + 54 kg × v_final = 0
Simplifying the equation, we can solve for the final velocity of the machine:
54 kg × v_final = -2.166 kg·m/s
v_final = -2.166 kg·m/s ÷ 54 kg
≈ -0.04 m/s
The negative sign indicates that the final velocity of the machine is in the opposite direction to the initial velocity of the tennis ball. In this case, the final velocity of the machine is approximately 0.04 m/s to the south.
Therefore, the final velocity of the machine is approximately 0.04 m/s to the south.