A quarterback claims that he can throw the football ahorizontal distance of 183 m (200 yd). Furthermore, he claims thathe can do this by launching the

asked 2021-02-16
A quarterback claims that he can throw the football ahorizontal distance of 183 m (200 yd). Furthermore, he claims thathe can do this by launching the ball at the relatively low angle of 30.0 degree above the horizontal. To evaluate this claim, determinethe speed with which this quarterback must throw the ball. Assumethat the ball is launched and caught at the same vertical level andthat air resistance can be ignored. For comparison, a baseballpitcher who can accurately throw a fastball at 45 m/s (100 mph)would be considered exceptional.

Answers (1)

For horizontal range of a projectile \(\displaystyle{R}={{V}_{{{0}}}^{{{2}}}}\frac{{\sin{{20}}}}{{g}}\) Hence \(\displaystyle{V}{0}=\sqrt{{{R}\cdot\frac{{g}}{{\sin{{20}}}}}}=\sqrt{{{183}\cdot\frac{{9.8}}{{\sin{{60}}}}}}={45.5}\frac{{m}}{{s}}\)
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