Question

A quarterback claims that he can throw the football a horizontal dis- tance of 183 m (200 yd). Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 30.08 above the horizontal. To evaluate this claim, determine the speed with which this quarterback must throw the ball.

Answer 1

Vo = 45.93m/s

Step-by-step explanation:

On the x-axis, we know that:

Xf = D = Vo*cos β * t where D = 183m and β=30.08°

Solving for t:

`t = (D)/(Vo*cos \beta )`

On the y-axis:

`Yf = Vo*sin \beta  * t - 1/2*g*t^2` Replacing our previous value for t:

`Yf = 0 = D*tan \beta -1/2*g*(D^2)/(Vo^2*cos^2\beta )`

Solving for Vo and using
`g=10m/s^2`:

`Vo = \sqrt{(g*D)/(2*sin\beta *cos\beta )} =45.93m/s`