Energy and Constant Acceleration Problem?

[donwa83]

Lazy Flee!

A lazy flee desires to jump across a log of radius R. It wants to find the most efficient way possible to do so. Find the initial velocity, distance from the radius of the log, and angle so that the above condition is true.

 

[Shooting Star]

How much have you done so far? You have not shown any of your work. Can you set up an equation for the path of the flea as in projectile motion?

 

[donwa83]

I am not entirely sure on how to begin and I'm also new to this forum so sorry for the bad formatting.

I have 6 constant acceleration equations by breaking up the following equations into vector equations that correspond to x and y.

Vf = Vo + at
$$V^{2}$$ = $$Vo^{2}$$ + 2a(d)
d = do + $$Vo^{2}$$ + (1/2)a $$t^{2}$$

I know that the flee's path is symmetrical so the final velocity equals the initial velocity. Since I have 7 unknowns, I should be able to solve it with 7 equations, but I only have 6. Besides using constant acceleration, should I also use Forces so that I can use the radius 'R,' which is given?

Thanks for your help.

 

[Shooting Star]

(It's spelled "flea". Flee is what many people want to do when given a problem like this one.)

The motion happens in a plane, which can be taken as the x-y plane, with y-axis in the vertical dircn. So, you don't need 6 eqns. Suppose the initial speed is u (your V0), making an angle 'b' with the horizontal. Then you can derive the eqn of the parabola in terms of u and b. It's simpler to deal with projectile motion this way.

The flea also wants to expend the least energy, which means that the initial KE (1/2)mu^2 is least, which means u^2 is least, given the other conditions.

The other conditions are:
i) it must clear the height of 2R
ii) it must not collide with the log.

First you should derive the eqn of the parabola, that is, the path of the flea.