Question

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?

Answer 1

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.