Dynamics - Motion in a Plane, Problem

[doctorjuice]

Homework Statement

A 5000kg rocket is launched at 44.7º with a thrust of 140,700N.
a. Find an equation y(x) that describes the rocket's trajectory.
b. Shape of trajectory?
c. At what elevation does the rocket reach the speed of sound, 330m/s?

Homework Equations

F=ma
The distance, acceleration, and velocity formulas.

The Attempt at a Solution

First, I found the acceleration = 22.36 m/s^2 (this is after including gravity).

I drew a triangle and calculated the acceleration's x and y components. acceleration of x comp. = 20 m/s^2. acceleration of y comp. = 10 m/s^2 (including gravity).

Using these acceleration x and y components, I found the x and y components for distance:
distance of x comp. = 2.486t. distance of y comp. = 1.131t.

For part a:
So, I wasn't sure exactly what they wanted for part a but this is what I did. The answer in the back of the book says y=(1/2)x, so I'm guessing they want the distance of y as a function of x (which is what the answer was). I'm not sure how to do that.

For part b:
I figured the shape of the trajectory would be parabolic since it is constantly accelerating. I thought trajectory was only a straight line if velocity was constant?

For part c:
Using my equations, I calculated it to be 37.32m, which is not correct.

Any help would be greatly appreciated, I'm doing these in preparation for a test and I really need to understand these type of problems.

 

[haruspex]

acceleration of x comp. = 20 m/s^2. acceleration of y comp. = 10 m/s^2 (including gravity).

Using these acceleration x and y components, I found the x and y components for distance:
distance of x comp. = 2.486t. distance of y comp. = 1.131t.

That doesn't look right. How did you calculate those?

For part a: I'm guessing they want the distance of y as a function of x (which is what the answer was).

Once you have correct expressions for x and y as functions of t, just eliminate t between them.

For part b:
I figured the shape of the trajectory would be parabolic since it is constantly accelerating. I thought trajectory was only a straight line if velocity was constant?

No. If y = f(t) and x = 2*f(t) then x = 2y for all t.