How Do You Calculate Projectile Motion in Football?

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To calculate projectile motion in football, the quarterback's throw can be analyzed by breaking the velocity into vertical and horizontal components, using the initial angle of 37 degrees. The horizontal motion can be described with the equation for distance, while the vertical motion involves determining the maximum height and time to reach that height. The initial speed of the ball, time to reach the receiver, and the highest point of the ball's flight can all be expressed in terms of the initial velocity (v) and angle (theta). The discussion highlights the need for substitution to solve for these variables, particularly focusing on the relationships between them. Understanding these concepts is essential for accurately calculating projectile motion in sports scenarios.
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Homework Statement


A quarterback throws the football to a stationary reciever who is 40.0m down the field. If the football is thrown at an initial angle of 37.0 degrees to the ground,
a. What is the initial speed of the ball?
b. How much time does it take for the ball to reach the reciever?
c. What is the ball's highest point during its flight.


Homework Equations


I took these images from wikipedia... Couldn't figure out that whole LaTeX thing.
122b1743350726387f11e0c0977d1abf.png

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4507e8151d7f4b9a5e7ea5ecc9599f56.png

ac74922e1ee9d3629919dbbeac1fcdff.png


The Attempt at a Solution


Well, I didn't get far. I figured you could break the ball's velocity into 2 parts, the vertical motion and horizontal motion, yielding vsin37 for vertical and vcos37 for horizontal motion. However, I don't know what value v is. I'm thinking that substitution will have to be used but I'm not sure where to go from here. I could really use some help! Thanks!
 
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Suppose v is the original velocity... what is the time it takes the ball to get to its maximum height in terms of v and theta? what is the time it takes the ball to get to 40.0m in terms of v and theta?
 

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