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- Homework Statement
- Rock is thrown at an angle and speed so that he almost touches three walls. Distance between walls are r and 2r (from left). Wall in the middle is two times higher than two other equal walls. Rock's flight range is nr. Find n.

- Relevant Equations
- kinematic eqs.

I tried to write a trajectory equation of motion.$$x(t)=vcos\alpha t$$

$$y(t)=vsin\alpha t-\frac{1}{2}gt^{2}$$from these we get:$$y=xtan\alpha -\frac{x^{2}g(1+tan^{2}\alpha )}{2v^{2}}$$For this problem:$$h=xtan\alpha -\frac{x^{2}g(1+tan^{2}\alpha )}{2v^{2}}$$ $$2h=(x+r)tan\alpha -\frac{(x+r)^{2}g(1+tan^{2}\alpha )}{2v^{2}}$$ $$h=(x+3r)tan\alpha -\frac{(x+3r)^{2}g(1+tan^{2}\alpha )}{2v^{2}}$$ $$0=nrtan\alpha-\frac{(nr)^{2}g(1+tan^{2}\alpha )}{2v^{2}} \Rightarrow tan\alpha= \frac{nrg(1+tan^{2}\alpha )}{2v^{2}}$$ So, we have 4 equations and 5 unknowns (x, tanα, v, h, n) and I stuck at solving them. May somebody can help?

I have an idea of adding $$nr=\frac{v^{2}sin2\alpha }{g}.$$ But then I surely don't know how to solve it.

Also, can we approximate that $$tan\alpha =\frac{h}{x} ?$$ I believe that would help solving this problem.