A tennis player places a 68kg ball machine on a frictionless surface. the machine fires a 0.057 kg tennis ball horizontally with a velocity of 38m/s toward the north. What is the final velocity of the machine?

I used p1+p2=P1'+p2' but I can't seem to get a correct answer.

The sum of momentum change is zero

Initial+Final=0
.057*38+68*V=0
solve for V. The negative sign means it is in the opposite direction as the original v.

the tennis ball and the machine have the same momentum, but in opposite directions

... Newton's 3rd law

68 * v = 0.057 * 38

TWO significant figures

M1 = 68kg, V1 = ?.

M2 = 0.057kg, V2 = 38 m/s.

M1*V1 = -M2*V2.
68*V1 = -(0.057*38),
V1 =

To solve this problem, we can 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, provided that no external forces act on the system.

Let's consider the tennis ball and the ball machine as the system. Since there are no external forces acting on the system, the total momentum before firing the ball is equal to the total momentum after the ball is fired.

Initially, the ball machine is at rest, so its momentum is zero (p1 = 0 kg·m/s). The tennis ball has a mass of 0.057 kg and a velocity of 38 m/s toward the north, so its initial momentum is given by:

p2 = mass × velocity = 0.057 kg × 38 m/s = 2.166 kg·m/s

After firing the ball, both the ball and the machine will have some final velocities. Let's assume the final velocity of the tennis ball is vf and the final velocity of the machine is Vf.

According to the principle of conservation of momentum:

total initial momentum = total final momentum
p1 + p2 = p1' + p2'

Since p1 = 0 kg·m/s, the equation becomes:

p2 = p1' + p2'

Substituting the values:

2.166 kg·m/s = 0 kg·m/s + p2'

Therefore, the final momentum p2' of the ball machine is equal to 2.166 kg·m/s.

To find the final velocity of the machine (Vf), we can use the formula:

momentum = mass × velocity
p2' = mass × Vf

Rearranging the equation:

Vf = p2' / mass
Vf = 2.166 kg·m/s / 68 kg
Vf ≈ 0.032 kg·m/s

Therefore, the final velocity of the machine is approximately 0.032 m/s toward the north.