Ball

Ball was fired at an angle of 35° at initial velocity 437 m/s. Determine the length of the litter. (g = 9.81 m/s²).

Correct result:

x =  18292.8 m

Solution:

$$\begin{gathered} v=437m\mathrm{/}s \\ {v}_x=v\cos 35^{\circ }=357.97m\mathrm{/}s \\ {v}_y=v\sin 35^{\circ }=250.65m\mathrm{/}s \\ x(t)=v_{x}t \\ y(t)=vt\sin 35^{\circ }-{\displaystyle \frac{1}{2}}g{t}^2 \\ y(t)=0 \\ vt\sin 35^{\circ }={\displaystyle \frac{1}{2}}g{t}^2 \\ t={\displaystyle \frac{2v\sin 35^{\circ }}{g}}=51.1015s \\ x=v_x\cdot t=357.97\cdot 51.1015=18292.8\text{ m} \end{gathered}$$

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