A baseball pitcher delivers a fastball that crosses the plate with an angle of 7.89 degrees relative to the horizontal and a speed of 87.5 mph. The ball (mass 0.145 kg) is hit back over the head of the pitcher at an angle of 38.03 degrees with respect to the horizontal and a speed of 105.5 mph. What is the magnitude of the impulse received by the ball?
To find the magnitude of the impulse received by the ball, we need to calculate the change in momentum.
The momentum of an object is given by the formula:
Momentum = mass x velocity
Initially, when the pitcher throws the ball, the momentum can be calculated using the given mass and speed of the ball. We can convert the speed from mph to m/s by dividing it by 2.237, since 1 mph is approximately equal to 0.447 m/s.
Initial momentum = mass x initial velocity
mass = 0.145 kg (given)
initial velocity = 87.5 mph = (87.5 / 2.237) m/s
Now, let's calculate the initial momentum.
initial momentum = 0.145 kg x (87.5 / 2.237) m/s
Next, when the ball is hit back by the batter, we need to calculate the final momentum. Again, we can convert the speed from mph to m/s.
final momentum = mass x final velocity
mass = 0.145 kg (given)
final velocity = 105.5 mph = (105.5 / 2.237) m/s
Now, let's calculate the final momentum.
final momentum = 0.145 kg x (105.5 / 2.237) m/s
To find the magnitude of the impulse, we need to calculate the change in momentum, which is the difference between the initial and final momentum.
change in momentum = final momentum - initial momentum
Finally, we can find the magnitude of the impulse by calculating the absolute value of the change in momentum.
magnitude of impulse = | change in momentum |
Do note that the values used in this explanation are based on the given information. You can replace them with actual numerical values to get the final answer.