If a jumping frog can give itself the same initial speed regardless of the direction in which it jumps (forward or straight up), how is the maximum vertical height to which it can jump related to its maximum horizontal range rmax = v20/g?

Explanation:

If u is the initial velocity at an angle \theta with horizontal then

Horizontal range of Frog can be given by

where u=initial velocity

a=acceleration

t=time

Here initial horizontal velocity

and there is no acceleration in the horizontal motion

Therefore

Considering vertical motion

here Initial vertical velocity

acceleration

for complete motion Y=0 i.e.displacement is zero

Therefore Range is

Range will be maximum when

and Maximum height

for

Divide 1 and 2

neither accurate nor precise.