Projectile problem

**Lucymathgirl** · March 3rd 2009, 04:27 PM

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?

**skeeter** · March 3rd 2009, 04:39 PM

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 $\theta$

**Lucymathgirl** · March 3rd 2009, 05:06 PM

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.

**skeeter** · March 3rd 2009, 05:13 PM

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 ... $t = \frac{12.5}{\cos{\theta}}$

**Lucymathgirl** · March 3rd 2009, 05:29 PM

oh right, thank you, so now how do i solve for t or theta?

**skeeter** · March 3rd 2009, 05:31 PM

substitute the corrected expression for $t$ in the $\Delta y$ equation, then solve for $\theta$ .

**Lucymathgirl** · March 3rd 2009, 05:48 PM

are trig. identities required to solve for sin theta?

**skeeter** · March 4th 2009, 05:13 AM

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.

**Lucymathgirl** · March 4th 2009, 02:24 PM

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!

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