# An object is thrown with velocity v from the edge of a cliff above level ground. Neglect air resistance. In order for the object to travel a maximum horizontal distance from the cliff before hitting the ground, the throw should be at an angle theta with respect tot eh horizontal of

a) greater than 60 degrees above the horizontal
b) greater than 45 degrees but less than 60 degrees above the horizontal
c)greater than zero but less than 45 degrees above the horizontal
d)zero
e)greater than zero but less than 45 degrees below the horizontal

I know it's not d) or e). It's either b) or c). but I think it's c) to get the max distance.

If it were thrown from the ground, the optimum angle would be exactly 45 degrees. When thrown from a cliff, there is an added benefit to be gained by increasing the horizontal velocity component, since you get a certain amount of "free" free fall time because of the elevation. Therefore the answer is (d).

This is a good question for using intuition. It would take quite a while and a bit of calculus to do come up with a rigorous mathematical proof.

But if the answer is d) the object wouldn't go very far. Because we are expose to find the maximum horizontal distance.