The speed of the rock when it is at height h/4 is .
Explanation:
At maximum height the final velocity of the rock is equal to 0. Let u is the initial velocity of the rock. Using the conservation of energy to find it as :
.......(1)
We need to find the speed of the rock when it is at height h/4. Let v' is the speed. Using 3rd equation of motion as :
here a = -g and s = h/4
Using equation (1) :
So, the speed of the rock when it is at height h/4 is . Hence, this is the required solution.
Furthermore, the Pythagorean theorem works when the two added vectors are at right angles to one another - such as for adding a north vector and an east vector.