A missile

A missile is fired with a speed of 100 fps in a direction 30° above the horizontal. Determine the maximum height to which it rises. Fps foot per second.

Correct answer:

h =  127.421 ft

Step-by-step explanation:

$$\begin{gathered} v_0=100\text{ft/s} \\ \alpha =30{}^{\circ } \\ g=9.81{\text{m/s}}^2 \\ {v}_y=v_0\cdot \sin \alpha =v_0\cdot \sin 30°=100\cdot \sin 30°=100\cdot 0.5=50\text{ft/s} \\ {v}_x=v_0\cdot \cos \alpha =v_0\cdot \cos 30°=100\cdot \cos 30°=100\cdot 0.866025=86.60254\text{ft/s} \\ {v}_y-g\cdot t=0 \\ t=v_y/g=50/9.81=\frac{5000}{981}\doteq 5.0968\text{s} \\ h=v_y\cdot t-\frac{1}{2}\cdot g\cdot t^2=50\cdot 5.0968-\frac{1}{2}\cdot 9.81\cdot 5.0968^2=127.421\text{ft} \end{gathered}$$

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