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cookiecrumbzz

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This a question from projectile motion.

When a projectile is launched from the ground level and it falls back on the same (ground) level, the horizontal displacement is maximised if the angle of projection (with respect to the horizontal) is 45 degrees.

BUT when the projectile is launched from a height

My question is, what relation can we derive to determine

R is the horizontal displacement if the angle of projection at h were 45 degrees.

__This is NOT "homework"__; it's a concept that got me thinking.When a projectile is launched from the ground level and it falls back on the same (ground) level, the horizontal displacement is maximised if the angle of projection (with respect to the horizontal) is 45 degrees.

BUT when the projectile is launched from a height

*the ground, and it falls onto the ground level, the maximum horizontal displacement is covered if the angle of projection is slightly less than 45 degrees.*__above____[PLEASE SEE THE ATTACHED THUMBNAIL]__My question is, what relation can we derive to determine

*the angle*(w.r.t. the horizontal)**theta***at which the projectile should be launched***from that height h**so as to get*maximum horizontal displacement*That is, what is the relation between theta, h, R and M as per the illustration (attached)?**M**?R is the horizontal displacement if the angle of projection at h were 45 degrees.