Question

a football is kicked at 22 m/s at an angle of 40 degrees above horizontal on level ground. how far does it travel

Answer 1

Question 15952

From one side, one knows that

$$v _ {x} = v _ {0} \cos \varphi , S _ {x} = v _ {0} \cos \varphi T$$

For vertical motion,

$$S _ {x} = v _ {0} t \sin \varphi - \frac {g t ^ {2}}{2}$$

The ball reaches the maximum altitude, when $\frac{dS_x}{dt} = 0, \Rightarrow t_{1/2} = \frac{v_0\sin\varphi}{g}$ - this gives the half of the time of the flight, so the full time of the flight is

$$T = \frac {2 v _ {0} \sin \varphi}{g}$$

Hence, $S_{x} = \frac{2v_{0}^{2}\cos\varphi\sin\varphi}{g}\approx 194.36m$