A 70 kg person is riding on a frictionless skateboard at 5 m/s. A friend facing him throws a 5 kg ball toward him at 20 m/s. What is his final speed after catching the ball?
To find the final speed of the person after catching the ball, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces are acting on it. In this case, the person and the ball can be considered as a closed system because no external forces, such as friction, are mentioned.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) can be calculated as:
p = mass x velocity
Given that the person has a mass of 70 kg and is traveling at 5 m/s, their initial momentum is:
Initial momentum of the person = mass of the person x velocity of the person
= 70 kg x 5 m/s
The ball has a mass of 5 kg and is thrown at a velocity of 20 m/s, so its initial momentum is:
Initial momentum of the ball = mass of the ball x velocity of the ball
= 5 kg x 20 m/s
Since no external forces are acting on the system, the total momentum before the catch is equal to the total momentum after the catch.
Total initial momentum = Total final momentum
Initial momentum of the person + initial momentum of the ball = Final momentum of the person + Final momentum of the ball
(70 kg x 5 m/s) + (5 kg x 20 m/s) = Final momentum of the person + (5 kg + 70 kg) x Final velocity
Now we can solve for the final velocity of the person:
Final velocity of the person = [(70 kg x 5 m/s) + (5 kg x 20 m/s)] / (5 kg + 70 kg)
Simplifying this equation gives us:
Final velocity of the person = (350 kg⋅m/s + 100 kg⋅m/s) / 75 kg
Final velocity of the person = 450 kg⋅m/s / 75 kg
Final velocity of the person = 6 m/s
Therefore, the person's final speed after catching the ball is 6 m/s.