A punter drops a .43 kg football from rest vertically 1 meter down onto his foot. The ball leaves his foot with a speed of 18m/s at an angle of 55* above the horizontal. What is the impulse delivered by the foot (magnitude and direction)?

To find the impulse delivered by the foot, we need to calculate the change in momentum of the football.

The impulse is defined as the product of force and time, or the change in momentum of an object. In this case, impulse can be calculated using the equation:

Impulse = Change in Momentum = Final Momentum - Initial Momentum

We need to calculate the magnitude and direction of the impulse. To do this, we will break down the impulse into its horizontal and vertical components.

First, let's calculate the initial momentum of the football. The initial momentum is given by:

Initial Momentum = Mass * Initial Velocity

The mass of the football is given as 0.43 kg, and the question states that the football is dropped from rest, which means the initial velocity is zero.

Initial Momentum = 0.43 kg * 0 m/s = 0 kg m/s

Next, let's calculate the final momentum. The final momentum is given by:

Final Momentum = Mass * Final Velocity

The mass of the football is still 0.43 kg, and the question states that the ball leaves the foot with a speed of 18 m/s at an angle of 55° above the horizontal. Therefore, we need to calculate the horizontal and vertical components of the final velocity.

Horizontal Component of Velocity = Final Velocity * cos(angle)
Vertical Component of Velocity = Final Velocity * sin(angle)

Using trigonometric functions, we can find:

Horizontal Component of Velocity = 18 m/s * cos(55°)
Vertical Component of Velocity = 18 m/s * sin(55°)

Now, we can calculate the final momentum:

Final Momentum = Mass * (Horizontal Component of Velocity + Vertical Component of Velocity)

Finally, we can find the change in momentum (impulse) by subtracting the initial momentum from the final momentum:

Impulse = Final Momentum - Initial Momentum

To find the magnitude and direction of the impulse, we need to calculate the horizontal and vertical components of the impulse:

Horizontal Component of Impulse = Impulse * cos(angle)
Vertical Component of Impulse = Impulse * sin(angle)

By substituting the calculated impulse and angle values, we can determine the magnitude and direction of the impulse delivered by the foot.