You are standing a horizontal distance of 140 m from a high

You are standing a horizontal distance of 14.0 m from a high fence. The top of the fence is 5.00 m above the ground. The ground is level, and the width of the fence is small enough to be ignored. You throw a rock from a height of 1.60 m above the ground and at an angle of 56.0 degrees above the horizontal. What minimum initial speed must the rock have as it leaves your hand to clear the top of the fence?

Solution

to just clear the fence, rock have to travel 5 - 1.6 = 3.4 m in vertical in the same time
it traveled 14m in horizontal.

suppose initial velocity was v.

then in horizontal, d = v_x * t

14 = (vcos56)t

vt = 25.04

in vertical, h = u_yt + at^2/2

3.4 = (vsin56t) - (9.81t^2 /2)

3.4 = 0.83vt - 4.9t^2

3.4 = 0.83*25.04 - 4.9t^2
t = 1.88 sec

v = (25.04/1.88) = 13.30 m/s