During a circus act, an elderly performer thrills the crowd by catching a cannon ball shot at him. The cannon ball has a mass of 10.0 kg and the horizontal component of its velocity is 8.00 m/s when the 65.0-kg performer catches it. If the performer is on nearly frictionless roller skates, what is his recoil velocity?

1.07

mass of ball x velocity/ mass of ball +mass of performer

To find the recoil velocity of the performer, we can use the principle of conservation of momentum. According to this principle, the total momentum before the event is equal to the total momentum after the event.

Let's denote the recoil velocity of the performer as V (positive to the right). The initial momentum of the cannonball is given by:

M1 = mass of the cannonball × horizontal component of its velocity
= 10.0 kg × 8.00 m/s
= 80.0 kg·m/s

The initial momentum of the performer + cannonball system is zero since the performer is initially at rest. Therefore, the initial total momentum is zero.

The final momentum of the cannonball + performer system is given by:

M2 = mass of the cannonball × recoil velocity of the performer
= 10.0 kg × V

According to the conservation of momentum principle, the initial total momentum is equal to the final total momentum. Therefore:

M1 = M2

This leads to the equation:

80.0 kg·m/s = 10.0 kg × V

Now we can solve for the recoil velocity V:

V = 80.0 kg·m/s / 10.0 kg
= 8.00 m/s

Hence, the recoil velocity of the performer is 8.00 m/s in the opposite direction of the cannonball's initial horizontal velocity.

To find the recoil velocity of the performer, we can apply the law of conservation of momentum.

According to the law of conservation of momentum, 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, we know the initial momentum of the cannon ball, and we want to find the final momentum of the performer.

The initial momentum of the cannon ball can be calculated using the formula:

Initial Momentum = Mass × Velocity

Given that the mass of the cannon ball is 10.0 kg and the horizontal component of its velocity is 8.00 m/s, we can calculate the initial momentum of the cannon ball.

Initial Momentum of the cannon ball = 10.0 kg × 8.00 m/s = 80.0 kg•m/s

Since there are no external horizontal forces acting on this system, the total initial momentum of the system is equal to the total final momentum of the system.

The final momentum of the system is given by:

Final Momentum = (Mass of the cannon ball + Mass of the performer) × Recoil Velocity

Given that the mass of the performer is 65.0 kg, and we want to find the recoil velocity, we can rearrange the equation to solve for the recoil velocity:

Recoil Velocity = Final Momentum / (Mass of the cannon ball + Mass of the performer)

Substituting the values, we have:

Recoil Velocity = 80.0 kg•m/s / (10.0 kg + 65.0 kg)

Recoil Velocity = 80.0 kg•m/s / 75.0 kg

Recoil Velocity = 1.07 m/s (rounded to two decimal places)

Therefore, the recoil velocity of the performer is approximately 1.07 m/s.