Solve 2D Motion Homework: Throw Football 196.6m at 25°

[IAmSparticus]

Homework Statement

A quarterback claims that he can throw the football a horizontal distance of 196.6 m (215 yd). Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 25° above the horizontal. To evaluate his claim, determine the speed with which this quarterback must throw the ball. Assume that the ball is launched and caught at the same vertical level and that air resistance can be ignored. For comparison, a baseball pitcher who can accurately throw a fastball at 45 m/s (100 mph) would be considered exceptional.

Homework Equations

delta x = V0x delta t

The Attempt at a Solution

70.93 m/s

Tried finding the maximum height the ball would reach by using 1/2 of the length (98.3) and then plug it into the max height equation : delta y = ((initial velocity)^2 sin (theta)^2)) / 2 acceleration of gravity (-9.8 m/s^2)

This would have given me the answer for the velocity needed sine the initial and final velocity would be the same in the x-direction.

 

[tiny-tim]

Welcome to PF!

Hi IAmSparticus! Welcome to PF!

Show us your full calculations, and then we can see what went wrong, and we'll know how to help.

Use the usual constant acceleration equations.

 

[tomcue]

However, this approach is incorrect since it does not take into account the initial velocity in the y-direction.

To find the correct answer, we can use the range equation: delta x = (initial velocity)^2 sin (2*theta) / acceleration of gravity (-9.8 m/s^2). Plugging in the given values, we get the initial velocity to be 70.93 m/s.

In conclusion, the quarterback would need to throw the football at a speed of 70.93 m/s in order to reach a horizontal distance of 196.6 m at an angle of 25° above the horizontal. This is a remarkable feat, as it is faster than the average speed of a professional baseball pitcher's fastball. However, it is not impossible, as there have been quarterbacks who have been able to achieve such speeds with their throws.