trajectory eq.

**jamessmith** · November 21st 2009, 11:57 AM

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.

**skeeter** · November 21st 2009, 12:21 PM

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.

$a_y = \frac{F_y}{m}$

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

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

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

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

**jamessmith** · November 21st 2009, 12:33 PM

Originally Posted by skeeter

$a_y = \frac{F_y}{m}$

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

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

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

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

How did you get the 1/2 in the 1/2*ay*t^2?

**Nevermind!** duh...

**skeeter** · November 21st 2009, 12:38 PM

Originally Posted by jamessmith

How did you get the 1/2 in the 1/2*ay*t^2?

two antiderivatives.

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