Question

Romeo is chucking pebbles gently up to juliet’s window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5 m below her window and 5.0 m from the base of the wall (Fig. 3-34).
How fast are the pebbles going when they hit her window?

Answer 1

so, if we name the takeoff point as (0,0) we want the vertex of the parabola to be at (5,4.5)

The parabola can thus be written as

y = -0.18(x-5)^2 + 4.5
so, at x=0, y' = 1.8

That means the initial angle is θ=60.9°

Now you should be able to work out the velocity components, and at the top of the arc, only the x component matters.