A 15 kg ball is thrown at a velocity of 20 km/hr to a 60 kg person who is at rest on ice. The person catches the ball and subsequently slides with the ball across the ice. Determine the velocity of the person and the ball after the collision*1 point1 km/hr2 km/hr3 km/hr4 km/hr
Question
A 15 kg ball is thrown at a velocity of 20 km/hr to a 60 kg person who is at rest on ice. The person catches the ball and subsequently slides with the ball across the ice. Determine the velocity of the person and the ball after the collision*1 point1 km/hr2 km/hr3 km/hr4 km/hr
Solution
This problem can be solved using the principle of conservation of momentum. The total momentum before the collision (the ball being thrown) is equal to the total momentum after the collision (the person sliding with the ball).
The momentum of an object is given by the product of its mass and velocity.
Before the collision, only the ball has momentum. Its mass is 15 kg and its velocity is 20 km/hr. We need to convert this velocity to m/s by multiplying by 1000/3600. So, the velocity in m/s is approximately 5.56 m/s. Therefore, the momentum of the ball is 15 kg * 5.56 m/s = 83.4 kg*m/s.
After the collision, both the person and the ball are moving together. Their total mass is 15 kg (ball) + 60 kg (person) = 75 kg.
Since the total momentum is conserved, the momentum after the collision is also 83.4 kgm/s. Therefore, we can find the velocity after the collision by dividing the total momentum by the total mass: 83.4 kgm/s / 75 kg = 1.112 m/s.
To convert this back to km/hr, we multiply by 3600/1000, giving a velocity of approximately 4 km/hr.
So, the person and the ball will be moving at a velocity of 4 km/hr after the collision.
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