How Do You Calculate the Impulse Received by a Football During a Kickoff?

[Sumbhajee]

Homework Statement

Calculate the impulse (in kg m/s) received by a football when it is kicked in a kickoff. The ball has a mass of 0.259 kg and travels a horizontal distance of 46 m. The ball is kicked at an angle of 47 degrees with the horizontal.
http://schubert.tmcc.edu/res/msu/mmp/kap6/picts/kick.gif

Homework Equations

Impulse= mass of ball * velocity final for ball

The Attempt at a Solution

I have tried solving this equation, but I cannot figure out how to find the final velocity of the ball. Any suggestions would be greatly appreciated. Thank you for your time. (It may be that the equation is incorrect.)

 

[Andrew Mason]

Homework Statement

Calculate the impulse (in kg m/s) received by a football when it is kicked in a kickoff. The ball has a mass of 0.259 kg and travels a horizontal distance of 46 m. The ball is kicked at an angle of 47 degrees with the horizontal.
http://schubert.tmcc.edu/res/msu/mmp/kap6/picts/kick.gif

Homework Equations

Impulse= mass of ball * velocity final for ball

The Attempt at a Solution

I have tried solving this equation, but I cannot figure out how to find the final velocity of the ball. Any suggestions would be greatly appreciated. Thank you for your time. (It may be that the equation is incorrect.)

You have to determine the velocity of the ball at launch from the data provided. This is a projectile trajectory problem but in reverse: you are given the trajectory distance and initial direction and you have to find the initial speed.

What is the relationship between range, launch angle and launch speed?

AM

 

[tomcue]

I would first like to clarify that the given equation for impulse is incorrect. The correct equation for impulse is Impulse= change in momentum, which can also be written as Impulse= mass * change in velocity.

To calculate the impulse received by the football, we must first find the final velocity of the ball. This can be done using the equations of motion for projectile motion. We know that the ball is kicked at an angle of 47 degrees with the horizontal, so we can break down the initial velocity into its horizontal and vertical components. The initial velocity in the horizontal direction (Vx) will remain constant throughout the motion, while the initial velocity in the vertical direction (Vy) will change due to the acceleration of gravity. We can use the equation Vf= Vi + at to find the final velocity in the vertical direction, where Vf is the final velocity, Vi is the initial velocity, a is the acceleration due to gravity (9.8 m/s^2), and t is the time of flight. We can also use the equation x= Vix * t to find the time of flight, where x is the horizontal distance traveled and Vix is the initial velocity in the horizontal direction. Once we have the final velocity in both the horizontal and vertical directions, we can use the Pythagorean theorem to find the magnitude of the final velocity.

After finding the final velocity, we can then calculate the change in velocity (Vf-Vi) and multiply it by the mass of the ball to find the impulse received by the football. This would give us the answer in kg m/s, as requested in the problem.

I hope this helps and clarifies any confusion. It is important to use the correct equations and understand the concepts behind them in order to accurately solve physics problems.