30. A quarterback claims that he can throw the football a horizontal distance of 183 m (200 yd). Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 30.0° 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.

 

To get the time of flight we use the change of height which is zero if the ball is caught at the same height it is thrown.

 

The product of two items being zero means either one is zero, so either t = 0, starting time

0r

Now we consider the horizontal motion

 

Plug in for time

 

Let’s use a trig identity that   using this produces

 

 

You may recognize this as the “Range” formula.  Now we solve for

 

 

 

Not too different from pitcher doing 45.0 m/s

 

 

 

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This page last updated on January 11, 2020