Question

A projectile is fired from the edge of a 200 m high Cliff with an initial velocity of 180m/s at an angle of 30 with the horizontal,find a,the horizontal distance from the gun to the point where the projectile strikes the ground and the greatest elevation above the ground reached by the projectile

Answer 1

Vertical problem first:
v = 180 sin 30 - 9.81 t = 90 - 9.81t
at peak v = 0
so at peak
9.81 t = 90
t = 9.17 seconds to top (wow)
h = 200 + 90 t - 4.9 t^2
so at top h = 200 + 90 (9.17) - 4.9 * 84.2
= 200 + 825 - 413 = 612.42 meters above ground
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Now horizontal
u = 180 cos 30 = 156 meters/second forever
range = 156 * time in the air
how long to ground though?
back to vertical problem
h = 200 + 90 t - 4.9 t^2
for h = 0
4.9 t^2 - 90 t - 200 = 0
solve quadratic for t = time in the air
then
range = 156 t