Question

A toy rocket is launched from the ground at an angle of 45° and an initial velocity of 100 feet

per second. How far does the rocket travel in the air before hitting the ground?

A. 170.7 ft
B. 213.4 ft
C. 312.4 ft
D.423.1 ft

Answer 1

`\textit{Horizontal Range}\\\\ R=\cfrac{(v_0)^2\cdot \sin(2\theta )}{g} ~~ \begin{cases} v_o=\textit{initial velocity}\\ \theta =\textit{initial angle}\\ g=gravity\\[-0.5em] \hrulefill\\ v_o=100\\ \theta =45^o\\ g\approx 32~(ft)/(s^2) \end{cases}\implies R\approx\cfrac{(100)^2 \sin(2\cdot 45^o)}{32} \\\\\\ R\approx\cfrac{10000\sin(90^o)}{32}\implies R\approx\cfrac{10000(1)}{32}\implies R\approx 312.5~ft`