- #1

compaq65

- 17

- 9

- 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.