A large boulder rests on a cliff 525 m above a small village in such a position

Question

A large boulder rests on a cliff 525 m above a small village in such a position that, if it should slide off, it would fall in the middle of the pond. The pond lies 100 m from the base of the cliff and has a width of 150 m.

Here the link to the image: http://s16.postimg.org/neiqu37x1/village.gif

In the figure shown above, the angle ? is 40°.
What is the initial speed of the boulder as it leaves the cliff?

I'm confused as to how your suppose to find the intial velocity when you don't know L=?m. Any pointer or help is greatly appreciated.

A large boulder rests on a cliff 525 m above a small village in such a position that, if it should slide off, it would fall in the middle of the pond. The pond lies 100 m from the base of the cliff and has a width of 150 m. In the figure shown above, the angle ? is 40degree. What is the initial speed of the boulder as it leaves the cliff? I'm confused as to how your suppose to find the intial velocity when you don't know L=?m. Any pointer or help is greatly appreciated.

Explanation / Answer

Let initial speed=U

Ux=Ucos40; Uy=Usin40.

let time taken by it to fell into lake=t

distance travelled in x-direction=100+150/2=100+75=175m.

distance travelled in y-direction=525m.

So, in x-direction,

Ucos40*t=175m or t=175/Ucos40.

in y-direction,

Usin40*t + 0.5gt^2=525.

substituting value of t in this eqn

175tan40+0.5*9.8*(175/Ucos40)^2=525.

solving this we have U=26m/s.

hence speed=26m/s.

So,it can be found without knowing L.

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