a projectile is fired at an angle of 27 above the horizontal from the top of a cliff 500 ft high. The initial speed of projectile is 1670 ft/s. How far will it move horizontally before hitting the level ground at the base of the cliff?

Answer 1

g = about 32 feet/second^2 as I remember from my childhood
so (1/2) g = 16

vertical problem
Vi = 1670 sin 27
Hi = 500

h = Hi + Vi t - 16 t^2

0 = 500 + (1670 sin 27) t - 16 t^2
solve quadratic for t, use the positive answer, that is time in the air

horizontal problem
u = 1670 cos 27 forever
range = u t