# Thread: trajectory eq.

1. ## trajectory eq.

A 500 kg space shuttle is moving along the x axis at 4 m/s. The rocket of the shuttle is fired, and it gives the shuttle a thrust of 1500 j-hat N. The rocket fires over a span of 2 seconds. How do I find the trajectory equation of the shuttle for the time the rocket is fired over the two seconds. I am supposed to do it with y = function of x.

2. Originally Posted by jamessmith
A 500 kg space shuttle is moving along the x axis at 4 m/s. The rocket of the shuttle is fired, and it gives the shuttle a thrust of 1500 j-hat N. The rocket fires over a span of 2 seconds. How do I find the trajectory equation of the shuttle for the time the rocket is fired over the two seconds. I am supposed to do it with y = function of x.
$\displaystyle a_y = \frac{F_y}{m}$

$\displaystyle a_y = \frac{1500}{500} = 3$

$\displaystyle y = \frac{1}{2}a_y t^2$ , $\displaystyle 0 \le t \le 2$

$\displaystyle y = \frac{3}{2}t^2$

since $\displaystyle x = 4t$ , substitute $\displaystyle \frac{x}{4}$ for $\displaystyle t$ into the equation for $\displaystyle y$

3. Originally Posted by skeeter
$\displaystyle a_y = \frac{F_y}{m}$

$\displaystyle a_y = \frac{1500}{500} = 3$

$\displaystyle y = \frac{1}{2}a_y t^2$ , $\displaystyle 0 \le t \le 2$

$\displaystyle y = \frac{3}{2}t^2$

since $\displaystyle x = 4t$ , substitute $\displaystyle \frac{x}{4}$ for $\displaystyle t$ into the equation for $\displaystyle y$
How did you get the 1/2 in the 1/2*ay*t^2?

**Nevermind!** duh...

4. Originally Posted by jamessmith
How did you get the 1/2 in the 1/2*ay*t^2?
two antiderivatives.