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:

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

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