A quarterback claims that he can throw the football a horizontaldistance of 169.

Question

A quarterback claims that he can throw the football a horizontaldistance of 169.1 m (185 yd). Furthermore,he claims that he can do this by launching the ball at therelatively low angle of 30° 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.
1 m/s

Explanation / Answer

The football is thrown a horizontal distance of R = 169.1m The ball is launched at an angle of = 30oabove the horizontal Let the speed with which the quaterback must thrown the ballbe u. The horizontal distance travelled by the football is R = (u2 * sin2/g) Here,g = 9.8 m/s2 or u2= (R * g/sin2) or u = (R * g/sin2)1/2 or u = (169.1 * 9.8/sin(2 * 30o))1/2 or u = 43.74 m/s or u = 43.74 m/s

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