A(n) 0.491 kg football is thrown with a speed of 17.8 m/s. A stationary receiver catches the ball and brings it to rest in 0.0147 s.
What is the magnitude of the impulse de- livered to the ball?
Answer in units of kg · m/s
To find the magnitude of the impulse delivered to the ball, we can use the impulse-momentum principle, which states that the impulse is equal to the change in momentum of an object.
The formula to calculate impulse is given by:
Impulse = Change in momentum
Momentum is defined as the product of mass and velocity:
Momentum = mass × velocity
First, let's calculate the initial momentum of the football before it is caught by the receiver:
Initial momentum = mass × initial velocity
Plugging in the given values, the initial momentum of the football is:
Initial momentum = 0.491 kg × 17.8 m/s
Now, let's calculate the final momentum of the football when it comes to rest:
Final momentum = mass × final velocity
Since the ball comes to rest, the final velocity is 0 m/s. Therefore, the final momentum is:
Final momentum = 0.491 kg × 0 m/s = 0 kg·m/s
The impulse delivered to the ball is equal to the change in momentum:
Impulse = Final momentum - Initial momentum
Impulse = 0 kg·m/s - (0.491 kg × 17.8 m/s)
Calculating this expression, we can find the magnitude of the impulse delivered to the ball.