Two competing catapults launch pumpkins. Catapult A launches from a starting height of 10ft and an initial upward velocity of 45ft/sec. Catapult B launches from a starting height of 25ft and an initial upward velocity of 40ft/sec. Which pumpkin, A or B, achieves a greater maximum height?

For these projectiles,

where is the projectile's final velocity (which is 0 at maximum height), is its initial velocity, is the acceleration due to gravity, and is its initial height.

Let denote the maximum heights of pumpkins A and B, respectively. Then

So pumpkin A reaches a greater maximum height.