Answer :
To stop the 0.450 kg soccer ball kicked at 25.0 m/s, the goalie exerts a 215 N force. Using the impulse-momentum theorem, we find it takes approximately 0.05233 seconds for the ball to stop.
To calculate the time it takes for the goalie to stop the soccer ball, we first need to determine the ball's initial momentum and then use the impulse-momentum theorem. The initial momentum of the ball can be found using the formula
momentum (p) = mass (m) x velocity (v).
Given the mass of the soccer ball is 0.450 kg and it is kicked at 25.0 m/s east, the initial momentum is:
- p = 0.450 kg x 25.0 m/s = 11.25 kg{m/s} east
The impulse-momentum theorem states that the change in momentum (impulse) is equal to the average force applied multiplied by the time duration of that force (impulse = Force x time). Since the ball is coming to a stop, its final momentum will be zero. Therefore, the impulse is equal to the initial momentum of the ball.
The force exerted by the goalie is 215 N. Setting the impulse equal to the initial momentum and solving for time (t) gives us:
- 11.25 kgt{m/s} = 215 N x t
Divide both sides of the equation by 215 N to find the time:
- t = 11.25 kg{m/s} / 215 N
- t = 0.05233 seconds
Hence, it takes approximately 0.05233 seconds for the goalie to stop the ball.
