# Projectile problem

• Mar 3rd 2009, 04:27 PM
Lucymathgirl
Projectile problem
Hi - I'm needing help with this one - cannot quite get it. Thanks

An airplane in level flight at an altitude of 7000 m is moving at 500 m/s. At the moment it flies overhead, a ground missile is fired at a constant acceleration of 80 m/s/s. What aiming angle above the ground must be used to hit the airplane?
• Mar 3rd 2009, 04:39 PM
skeeter
Quote:

Originally Posted by Lucymathgirl
Hi - I'm needing help with this one - cannot quite get it. Thanks

An airplane in level flight at an altitude of 7000 m is moving at 500 m/s. At the moment it flies overhead, a ground missile is fired at a constant acceleration of 80 m/s/s. What aiming angle above the ground must be used to hit the airplane?

let $\theta$ be the launch angle above the horizontal

$a_x = 80\cos{\theta}$

$a_y = 80\sin{\theta}$

since acceleration is constant and initial velocity = 0 ...

$\Delta x = 500t = \frac{1}{2}a_x t^2$

$\Delta y = 7000 = \frac{1}{2}a_y t^2$

solve the system for $t$ and $\theta$
• Mar 3rd 2009, 05:06 PM
Lucymathgirl
mathing it out
Thanks - working it through, then, I can get for the horizontal that t=cos theta/12.5, and for the vertical that t squared = 175/sin theta. This is where I get stuck.
• Mar 3rd 2009, 05:13 PM
skeeter
Quote:

Originally Posted by Lucymathgirl
Thanks - working it through, then, I can get for the horizontal that t=cos theta/12.5, and for the vertical that t squared = 175/sin theta. This is where I get stuck.

correction ... $t = \frac{12.5}{\cos{\theta}}$
• Mar 3rd 2009, 05:29 PM
Lucymathgirl
oh right, thank you, so now how do i solve for t or theta?
• Mar 3rd 2009, 05:31 PM
skeeter
substitute the corrected expression for $t$ in the $\Delta y$ equation, then solve for $\theta$.
• Mar 3rd 2009, 05:48 PM
Lucymathgirl
are trig. identities required to solve for sin theta?
• Mar 4th 2009, 05:13 AM
skeeter
Quote:

Originally Posted by Lucymathgirl
are trig. identities required to solve for sin theta?

It seems from your responses that you are not confident in using your algebra and trig skills.

If such is the case, then I recommend you solve the equation using your calculator. If your calculator skills are wanting, then I advise that you have a face-to-face session with your instructor.
• Mar 4th 2009, 02:24 PM
Lucymathgirl
Thanks
Hi - yes, I am just learning this area of trig, but I think that I have it solved now. Thanks so much for your help!