A quarterback claims that he can throw the football a horizontaldistance of 196.

Question

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

Explanation / Answer

The formula for calculating the maximum horizontaldisplacement of a body,   with initial speed u,   launched at an angle with horizontal,   is : R = u*u*sin(2) / g = 196.6 m = 25` g = 9.8 m/s2    So, u = [196.6 * 9.8 / (sin(50))] = 50.15m/s which is greater than the limit 45 m/s

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