projectile motion
posted by tanaiah .
A missile is fired upwards from the top of a cliff in a direction making an angle (not known ) with the horizontal. After 20seconds the projectile hits the ground at a point which is 1800metre from the foot of the tower of height 160metres. Find the angle of projection and the initial velocity of the projection and the maximum height?

we know that the path follows
x(t) = v cosθ t
y(t) = 160 + v sinθ t  4.9t^2
I will assume that the cliff and the tower are the same, otherwise I'm confused.
x(20) = 1800
y(20) = 0
So,
20v cosθ = 1800
20v sinθ = 1800
Clearly θ = π/4 and v = 127.28 m/s
y = 160 + 90t  4.9t^2
so at t=9.18 the max height of 573.27m is attained.