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Range of a two dimensional project in Earth's gravitational field.

Horizontal speed = u Cos A

vertical speed initial = u Sin A

vertical velocity = v= u Sin A - g t v = 0, when t = u sin A/g

The projectile lands when t = 2 * u sin A / g.

Range = horizontal distance travelled = u CosA * 2u Sin A / g

R = u^2 Sin 2A / g

If u =20 m/s, and A = 45 deg for maximum range, for a given speed u:

R = 20 * 20 Sin(2*45) / 10 as g = 10 m/sec/sec

R = 20*2 Sin90 = 40 meters

Horizontal speed = u Cos A

vertical speed initial = u Sin A

vertical velocity = v= u Sin A - g t v = 0, when t = u sin A/g

The projectile lands when t = 2 * u sin A / g.

Range = horizontal distance travelled = u CosA * 2u Sin A / g

R = u^2 Sin 2A / g

If u =20 m/s, and A = 45 deg for maximum range, for a given speed u:

R = 20 * 20 Sin(2*45) / 10 as g = 10 m/sec/sec

R = 20*2 Sin90 = 40 meters