A projectile is fired from the top of a cliff of height h above the ocean below. The projectile is fired at an angle θ above the horizontal and with an initial speed vi.

(a) Find a symbolic expression in terms of the variables vi, g, and θ for the time at which the projectile reaches its maximum height.
(b) Using the result of part (a), find an expression for the maximum height hmax above the ocean attained by the projectile in terms of h, vi, g, and θ

Question

A projectile is fired from the top of a cliff of height h above the ocean below. The projectile is fired at an angle θ above the horizontal and with an initial speed vi.

(a) Find a symbolic expression in terms of the variables vi, g, and θ for the time at which the projectile reaches its maximum height.
(b) Using the result of part (a), find an expression for the maximum height hmax above the ocean attained by the projectile in terms of h, vi, g, and θ

jamesj · Answer

Well the initial velocity in the +y direction is
vy(t=0) = vi.sin(theta)

So it will be at the top when vy = 0 or when vi.sin(theta) - gt = 0, because the projectile is constantly accelerated in the negative y direction at a rate of g.

So 
t = vi.sin(theta)/g

Now try part b yrself!