# Rocket projectile motion problem [closed]

In a brisk wind from the south-east of $14.1\:\mathrm{m/s}$ a rocket pointed due north is launched from a cliff that is $500\:\mathrm{m}$ above the ground. The $1000\:\mathrm{kg}$ rocket is launched at an angle at $30º$ from the horizon. On launch the rocket's engine provides a thrust that decreases with time according to the following relationship:

Thrust ($\mathrm{N}) = 10000 (5-t)$, where t is in seconds.

You may ignore air resistance. Assume that the rocket's mass remains constant while the rocket engine is burning and that $g = 10\:\mathrm{m/s^2}$. Determine (i) where the rocket will land downrange, (ii) the apex of the rocket's flight, (iii) the position of the rocket after it is in flight for $10\:\mathrm{s}$ and (iv) the direction and magnitude of the rocket's velocity after it is in flight for $10\:\mathrm{s}$. State your answers using the appropriate displacement and velocity vectors in $\vec{i}$, $\vec{j}$, $\vec{k}$.

I started by trying to draw some diagrams in the different directions, but I couldn't visualize it. Since it mentions the three vectors, does that mean I have to split it into three system of equations, then solve the unknowns that way?

## closed as off-topic by user10851, Bill N, Kyle Kanos, Sebastian Riese, user36790 Oct 17 '15 at 1:25

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• It seems to be a relative velocity problem despite the statement "ignore air resistance." I guess that "air assistance" is important. consider that the acceleration is not constant. You have to integrate the acceleration to get the velocity, then integrate the velocity to get the position. – Bill N Oct 16 '15 at 19:11

As this is clearly a homework question I won't provide you with a full solution but because it's a fairly complicated problem I'll try and point you in the right direction.

Set up a reference frame of $x,y,z$ axis with origin at the point of launch, as in the diagram above.

The velocity vector $\vec{v}$ needs to be decomposed into three vectors $\vec{v_x}$, $\vec{v_y}$ and $\vec{v_z}$, which exist independently from each other.

Knowing these components allows to calculate the position vectors $\vec{x}$, $\vec{y}$ and $\vec{z}$, in time $t$.

There are two complications.

1) Wind: "You may ignore air resistance" to my mind means that the $x$ and $y$ components of $\vec{v_w}$ simply have to be added to $\vec{v_x}$ and $\vec{v_y}$, respectively. Wind thus causes the rocket to 'drift' away from the $x$ and $y$ axis.

2) Rocket burn time: your rocket motor only thrusts for $5\:\mathrm{s}$, so after $5\:\mathrm{s}$ the equations of motion change. You must therefore determine $\vec{x}$, $\vec{y}$ and $\vec{z}$ at $t=5\:\mathrm{s}$, then apply the new (no thrust) equations of motion to determine the final landing coordinates of the rocket.

• Thanks this is all I needed. Sorry for phrasing it in a way that I was asking for the answer. I just wanted a clear start (i.e. reference frame, and a clear understanding of the question). – user3657449 Oct 18 '15 at 19:06
• @user3657449: thanks but as you can see the question is now on 'hold', so without editing on your part it will be deleted (in a few days, I believe) – Gert Oct 18 '15 at 19:45