# Thread: Harder 3U - projectile motion question

1. ## Harder 3U - projectile motion question

From Patel 4U (Ex. 8B, Q5):

$A missile is fired from\, O\, with initial velocity\, U\, at an angle\, \alpha\, with the horizontal.\\\\ Prove that it describes a parabola of focal length\,\frac{U^2\cos^2\alpha}{2g}\,.\\\\ Also prove that any point\, P(x,y)\, within and on the circle\,x^2+y^2=\frac{v^4}{g^2}\, is in danger of being hit by the missile.$

I've got the first part but I'm stuck on the second part.

I'm not sure what $v$ means - maybe it's a typo and meant $U$.

2. ## Re: Harder 3U - projectile motion question

Yeah, I believe it’s a typo. Don’t think it refers to the instantaneous speed of the projectile, as that will unnecessarily complicate things.

So does that solve the problem, or do you still want the solution ?

3. ## Re: Harder 3U - projectile motion question

Originally Posted by KAIO7
Yeah, I believe it’s a typo. Don’t think it refers to the instantaneous speed of the projectile, as that will unnecessarily complicate things.

So does that solve the problem, or do you still want the solution ?
I still haven't figured it out yet... hints or a solution would be helpful.

4. ## Re: Harder 3U - projectile motion question

Well here are some hints: consider the range of the projectile to be the radius of the circle, and take into account the change in Alpha. Also focus on the part that says on the circle and within and see when that happens.

If you need further hints or a solution, let me know

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