# Projectile Motion Problem. Is my answer correct ?

• Diff.Ed
In summary, the problem is to find the angle at which a projectile should be launched in order to go from point A to B and miss a pole of height H, given that the distance between A and B is D. The solution involves finding the height h using the formula h=\frac{D\tan\alpha\tan\beta}{\tan\alpha+\tan\beta}, and then considering a particle falling freely from point B to the top of the pole. The final answer should be a function of the initial velocity, the angles of the inclines, and the height of the pole.

## Homework Statement

A projectile is to be launched so as to go from A to B [which are respectively at the bases of a double inclined plane having angles $\alpha$ and $\beta$ as seen in the figure] and just barely miss a pole of height $H$ that is located at the tip. If the distance between A and B is D, find the angle with the horizontal at which the projectile should be launched.

[PLAIN]http://b1111.hizliresim.com/r/k/llf5.jpg [Broken]

## The Attempt at a Solution

[PLAIN]http://b1111.hizliresim.com/r/k/llds.jpg [Broken]

I found $h=\frac{D\tan\alpha\tan\beta}{\tan\alpha+\tan\beta}$

and I considered a particle which is at B is falling free.And Vo vector aimed to point B when t=0 , so they must collide at $t=t_{collide}$ and at top of the H.
Then i wrote $\tan\phi=\frac{1/2gt_{collide}^2+H+h}{\frac{D\tan\beta}{\tan\alpha+\tan\beta}}$
and i found
$\phi= \tan^-1(\frac{(1/2gt_{collide}^2+H)(\tan\alpha+\tan\beta)+D\tan \alpha \tan\beta}{D\tan\beta})$

Is my answer is correct ? and are there any solutions for conditions which are before reaching maximum height and minumum height ?

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Your "answer" assumes you know the the time it will take the projectile to reach the top of the pole.

The answer should be a function of the initial velocity (V0), the angles of the inclines (α and β), and the height of the pole from the top of the incline (H).