# Maths - Projectile Motion using Calculus

a\A ball is hit from the ground with an innitial velocity of 25m/s into the air. It is to land in a hole that is 10m above the ground. Given this, I need to find the maximum horizontal distance that the hole can be away from the innitial position of the ball and the angle at which the ball must be hit to achieve this maximum distance. NOTE: neither the ball not the hole are situated on inclined planes. The ball is hit from a flat horizonatl surface and needs to land in a hole in another flat horizontal surface that is 10m higher than the original surface

I know that the maximum range when its landing is level with the innitial position is produced by a 45 degree angle, however I dont know how to calculate the maximum horizontal distance and what the angle needs to be to achieve this when the landing position is higher than the innitial position. Please someone explain. It must be done using CALCULUS (no air resitance so using basic projectile motion equations) and no dumb physics equations like s=ut + 1/2at^2 etc.

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