To find the speed with which the ball moves off after the penalty kick, we can use Newton's second law and the impulse-momentum principle.
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Calculate the impulse: Impulse is the product of force and the time over which the force acts. The impulse experienced by the ball can be calculated using the formula:
\[ \text{Impulse} = \text{Force} \times \text{Time} \]
Given:
- Force = 30 N
- Time = 0.05 s
\[ \text{Impulse} = 30 , \text{N} \times 0.05 , \text{s} = 1.5 , \text{Ns} \]
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Relate impulse to change in momentum: The change in momentum of the ball is equal to the impulse applied to it. The momentum \( p \) of an object is given by:
\[ p = m \times v \]
where \( m \) is the mass and \( v \) is the velocity. Here, we want to find the final velocity of the ball.
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Calculate the final velocity: Since the ball is initially at rest, the change in momentum is equal to the final momentum:
\[ \text{Impulse} = m \times v \]
Rearranging the formula to solve for \( v \):
\[ v = \frac{\text{Impulse}}{m} \]
Now substituting the values:
- Impulse = 1.5 Ns
- Mass \( m = 0.075 , \text{kg} \)
\[ v = \frac{1.5 , \text{Ns}}{0.075 , \text{kg}} = 20 , \text{m/s} \]
Thus, the speed with which the ball moves off is 20 m/s.
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