Projectile Motion - What angle should the quarterback throw the football?

• ElleElle
In summary, to throw a football at 22.0 m/s to a receiver 31.0 m away, the quarterback should angle it 19.4° above the horizontal. However, this solution may not be correct due to an error in the math.
ElleElle
A quarterback wants to throw a football at 22.0 m/s to a receiver 31.0 m away. At what angle above the horizontal should he throw it? Assume that the receiver catches the ball at the same height that the quarterback releases it.

The answer should be 19.4° but for some reason I just cannot get it!

I solved for time by using: x = xi + vit + (1/2)at^2
I got t = 1.13s

Then i used x = vt to solve for velocity in the y direction. vy = 27.5 m/s (which does not seem right)

Then cos θ = adj/hyp which gives me a math error :/

Treat the horizontal and vertical motions of the ball separately. To find the time, find the vertical component of the ball's velocity, and see how long it will take for the ball to reach its maximum height and come back down.

Last edited:
tms said:
Treat the horizontal and vertical motions of the ball separately. To find the time, find the vertical component of the ball's velocity, and see how long ti will take for the ball to reach its maximum height and come back down.

What formula would i use for the vertical component? Vf=Vi+at and Δy=Vit+(1/2)at^2 ?

Which do you think? You know, or can calculate, the initial vertical speed, you know the speed at the maximum height, you know the acceleration, and you want to find the time. Which equation will give you what you want knowing what you know?

Try this: Find an equation that gives you the time it takes to go up and down. Then find another equation that gives you the time it takes to get there in the horizontal direction. Hint: You are already given what x is. You will have two unknowns with two equations. Solve for target!
Your also going to need a trigonometry identity.

What is projectile motion?

Projectile motion is the motion of an object through the air that is influenced by gravity. This type of motion follows a parabolic path and can be seen in activities such as throwing a football or shooting a basketball.

What factors influence projectile motion?

The angle of release, initial velocity, and the effects of air resistance and gravity all influence projectile motion. These factors can affect the distance, height, and speed of the projectile.

What angle should the quarterback throw the football to achieve the maximum distance?

The optimal angle for maximum distance in projectile motion is 45 degrees. This angle allows for the greatest amount of horizontal distance while still accounting for the effects of gravity.

How does air resistance affect the trajectory of a football?

Air resistance, or drag, can cause the football to slow down and deviate from its desired path. It can also cause the ball to drop faster due to the upward force it creates. This is why quarterbacks often throw the ball at an angle to counteract the effects of air resistance.

Why is the angle of release important in projectile motion?

The angle of release determines the initial direction and trajectory of the projectile. A higher angle will result in a steeper trajectory and a shorter distance, while a lower angle will result in a flatter trajectory and a longer distance. The angle of release is crucial in achieving the desired outcome in projectile motion.

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