during a circus act, an elderly performer thrills the crowd by catching a cannon ball shot at him the ball mass is 10.0 kg and ball velocity is 8 m/s while the performer mass is 65 kg. if the performer is on nearly friction-less roller skates, what is his recoil velocity.
To find the recoil velocity of the performer, we can use the principle of conservation of momentum. According to this principle, in the absence of external forces, the total momentum before an event is equal to the total momentum after the event.
The total momentum before the event is given by the sum of the momentum of the cannonball and the momentum of the performer, which can be calculated as:
Momentum of cannonball = mass of cannonball * velocity of cannonball
Momentum of performer = mass of performer * velocity of performer
Using the given values:
Mass of cannonball = 10.0 kg
Velocity of cannonball = 8 m/s
Mass of performer = 65 kg
The total momentum before the event is:
Momentum before = (10 kg * 8 m/s) + (65 kg * 0 m/s) (since the performer is initially at rest)
As no external forces act on the system after the cannonball is caught, the total momentum after the event is:
Momentum after = (10 kg * 0 m/s) + (65 kg * recoil velocity)
Since the momentum is conserved, we have:
Momentum before = Momentum after
(10 kg * 8 m/s) + (65 kg * 0 m/s) = (10 kg * 0 m/s) + (65 kg * recoil velocity)
Simplifying the equation:
80 kg m/s = 65 kg * recoil velocity
Rearranging the equation to solve for the recoil velocity:
recoil velocity = 80 kg m/s / 65 kg
Calculating the recoil velocity:
recoil velocity ≈ 1.23 m/s
So, the recoil velocity of the performer on the nearly friction-less roller skates is approximately 1.23 m/s.
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 cannonball is caught should be equal to the total momentum after it is caught.
Let's assume that the initial velocity of the performer is zero (since they are at rest) and the recoil velocity is v.
Using the formula for momentum (momentum = mass × velocity), the initial momentum of the system is:
Initial momentum = mass of the cannonball × velocity of the cannonball
= 10.0 kg × 8 m/s
= 80.0 kg·m/s
The final momentum of the system is:
Final momentum = 0 kg × 0 m/s (since the performer is initially at rest and has zero momentum)
+ (mass of the cannonball + mass of the performer) × recoil velocity
= (10.0 kg + 65 kg) × v
= 75.0 kg × v
According to the conservation of momentum principle:
Initial momentum = Final momentum
Therefore, we can write:
80.0 kg·m/s = 75.0 kg × v
To find the value of v, we can rearrange the equation:
v = (80.0 kg·m/s) / (75.0 kg)
v ≈ 1.07 m/s
Therefore, the recoil velocity of the performer is approximately 1.07 m/s.