A 0.48 kg soccer ball approaches a player horizontally with a velocity of 18 m/s to the north. The player strikes the ball and causes it to move in the opposite direction with a velocity of 24 m/s.
What impulse was delivered to the ball by the player?
Answer in units of kg · m/s.
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To find the impulse delivered to the ball by the player, we can use the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. It is a vector quantity and its direction is the same as the direction of the velocity.
The initial momentum of the soccer ball can be calculated by multiplying its mass and initial velocity:
Initial momentum = Mass × Initial velocity
Given:
Mass of the soccer ball (m) = 0.48 kg
Initial velocity (v_initial) = 18 m/s (to the north)
Initial momentum = 0.48 kg × 18 m/s = 8.64 kg · m/s (to the north)
Now, after the player strikes the ball, it moves in the opposite direction with a velocity of 24 m/s:
Final velocity (v_final) = 24 m/s (opposite direction)
The final momentum of the soccer ball can be calculated by multiplying its mass and final velocity:
Final momentum = Mass × Final velocity
Final momentum = 0.48 kg × 24 m/s = 11.52 kg · m/s (to the south)
Impulse is defined as the change in momentum of an object. It can be calculated by subtracting the initial momentum from the final momentum:
Impulse = Final momentum - Initial momentum
Impulse = 11.52 kg · m/s (to the south) - 8.64 kg · m/s (to the north)
Impulse = 11.52 kg · m/s - 8.64 kg · m/s = 2.88 kg · m/s (to the south)
Therefore, the impulse delivered to the ball by the player is 2.88 kg · m/s, in the opposite direction to the initial velocity, which is to the south.