You have a cannon a distance \(d\) before the start of a hill. The hill goes up at an angle \(\theta\) from the ground. What angle and velocity must you shoot a cannon ball so that it lands a distance \(s\) up the hill?(The distance s is measured from the bottom of the hill, i.e. the distance along the hill).

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TopNewestI think there are infinite solutions to this problem. There are infinite parabolas passing through (0,0) and \((d+sCos\theta,sSin\theta)\), the cannon at (0,0). – Niranjan Khanderia · 1 year, 4 months ago

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This question is given to me by @Josh Silverman Sir. – Nihar Mahajan · 1 year, 4 months ago

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– Niranjan Khanderia · 1 year, 4 months ago

The above equation has two unknowns. Only one equation. Thus infinity solutions.Log in to reply

– Nihar Mahajan · 1 year, 4 months ago

Yes , that was what I was saying too.Log in to reply

– Calvin Lin Staff · 1 year, 4 months ago

Well, I believe that the gravitational field is fixed, so you may assume that acceleration is \(a\)....Log in to reply

– Krishna Sharma · 1 year, 4 months ago

Niranjan sir is right since angle and velocity both are upto us there are infinite possibilities.One of them has to be given for a finite(2 if velocity is given[not always]) number of solutions.Log in to reply

So, what is the relationship between \( \theta \) and \( v \)? – Calvin Lin Staff · 1 year, 4 months ago

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Hey guys, I've made this into a well-constrained problem, here – Josh Silverman Staff · 1 year, 4 months ago

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