A model rocket is launched from point A with an initial velocity v of 86 m/s. If the rocket's descent parachute does not deploy and the rocket lands 104m from A, determine (a)the angle that v forms with the vertical, (b)the maximum height h reached by the rocket, and (c)the duration of the flight.

Question

whpalmer4 · Answer

Height of the rocket will be $$h(t) = -\frac{1}{2}gt^2 + v_0 t\sin \theta  + h_0$$ where 
$\qquad g=9.8 \text{ m/s}^2$
$\qquad v_0 = 86 \text{ m/s}$
$\qquad h_0 = 0 \text{ m}$
$\qquad \theta = \text{ angle formed with the vertical}$

That's a parabola. You'll solve that for $h(t_f) = 0$ to find the time of flight.

The horizontal component of the rocket's velocity will be $v_x = v_0 \cos \theta$.  You know that $x = v_x t_f = 104 \text{ m}$ where $t_f$ is the time of flight.  You can use that relationship to write an expression for $t_f$ in terms of $v_0$ and $\theta$.  Substitute that into the first equation and solve for $\theta$.  

Once you've got the parabola figured out, you can easily find the maximum height by finding the vertex, and you've already found the duration of the flight.