A 0.45 kg football traveling at a speed of 22 m/s is caught by a stationary receiver. If the football comes to a rest in the receiver's arms, the magnitude of the impulse imparted to the receiver by the ball is
|m∆v| = 0.45*22 = ____kg-m/s
880
The magnitude of the impulse imparted to the receiver by the ball can be calculated using the principle of conservation of momentum. The impulse is equal to the change in momentum.
The momentum of an object is given by the product of its mass and velocity. In this case, the mass of the football is 0.45 kg and its velocity is 22 m/s. Therefore, the initial momentum of the football is:
Momentum = mass x velocity
= 0.45 kg x 22 m/s
= 9.9 kg·m/s
Since the receiver catches the football and brings it to rest, the final velocity of the football is 0 m/s. Therefore, the final momentum of the football is:
Final momentum = mass x final velocity
= 0.45 kg x 0 m/s
= 0 kg·m/s
The change in momentum is the final momentum minus the initial momentum:
Change in momentum = Final momentum - Initial momentum
= 0 kg·m/s - 9.9 kg·m/s
= -9.9 kg·m/s
Since impulse is equal to the change in momentum, the magnitude of the impulse imparted to the receiver by the ball is:
Magnitude of impulse = |Change in momentum|
= |-9.9 kg·m/s|
= 9.9 kg·m/s
Thus, the magnitude of the impulse imparted to the receiver by the ball is 9.9 kg·m/s.
To find the magnitude of the impulse imparted to the receiver by the football, we need to use the principle of conservation of momentum. The impulse is defined as the change in momentum, and momentum is given by the product of an object's mass and velocity.
The momentum of the football before being caught can be calculated as follows:
Momentum = mass * velocity
Given:
Mass of the football (m) = 0.45 kg
Velocity of the football (v) = 22 m/s
Momentum of the football before being caught = (0.45 kg) * (22 m/s) = 9.9 kg·m/s
Since the football comes to rest in the receiver's arms, its final velocity is zero. This means the final momentum of the football is also zero.
The impulse imparted to the receiver by the ball is equal to the change in momentum of the ball, which can be calculated as:
Impulse = Final Momentum - Initial Momentum
Impulse = 0 - 9.9 kg·m/s (since the final momentum is zero)
Impulse = -9.9 kg·m/s
Therefore, the magnitude of the impulse imparted to the receiver by the ball is 9.9 kg·m/s.