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## #1 2014-07-26 03:07:23

lukesean
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Registered: 2014-07-26
Posts: 1

### Challenging Applied maths question projectiles

An aircraft flies at a constant height H and constant velocity V. When the aircraft has flown directly over a gun on the ground a shot is fired from the gun which points at the aircraft at an angle of elevation Ѳ. If the initial velocity of the bullet is KVsecѲ [k >1], and Ѳ =tan inverse[ 1/V√gh/(k-1) ], show that the bullet hits the aircraft directly.

Please if any one can answer me this question I appreciate it a lot.

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## #2 2014-07-27 00:25:43

Nehushtan
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Registered: 2013-03-09
Posts: 905
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### Re: Challenging Applied maths question projectiles

When the shot is fired, the plane has travelled a horizontal distance
. (You can picture this by drawing a diagram.)

The time taken for the bullet to rise to height
is given by

I think the idea is to solve for
algebraically and show that
(horizontal distance travelled by bullet)
(distance travelled by plane after passing gun).

Last edited by Nehushtan (2014-07-27 00:49:03)

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## #3 2014-07-27 00:47:32

Nehushtan
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Registered: 2013-03-09
Posts: 905
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### Re: Challenging Applied maths question projectiles

Just solved it!

In solving algebraically for
you need to take the minus sign in front of the square root:

This value of
will work. In other words the bullet hits the plane on the way up rather than on the way down.

The computation is straightforward but tricky. You just need to take extra care not to make any careless mistake.

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