A quarterback claims that he can throw the football a horizontal distance of 162

Question

A quarterback claims that he can throw the football a horizontal distance of 162 m. Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 28.0 ° above the horizontal. To evaluate this 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.

Explanation / Answer

This is the case of projectile motion

Horizontal range of the projectile motion R is

R = v^2 * sin (2 * theta) / g

here,

R = 162 m

theta = 28 degree

putting values in the formula

162 = v^2 * sin (2 * 28) / 9.8

v = 43.76 m/s

the speed with which this quarterback must throw the ball = 43.76 m/s

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