You are launching Robin Hood out of a cannon and over the wall of the castle to rescue the Maid Marion. He would like to clear the castle wall by as much as possible. The cannon is stuck at an angle of 45 degrees from the ground and will launch him with a speed of 25 m/s. How close does he need to be to the wall to have the largest gap between him and the top of the wall as he flies over it?

Question

You are launching Robin Hood out of a cannon and over the wall of the castle to rescue the Maid Marion.  He would like to clear the castle wall by as much as possible. The cannon is stuck at an angle of 45 degrees from the ground and will launch him with a speed of 25 m/s.  How close does he need to be to the wall to have the largest gap between him and the top of the wall as he flies over it?

Steve · Answer

clearly he wants the vertex of the parabola to be just above the wall.

Recall that the trajectory can be described as

y = x tanθ - g/[2 v^2 cos^2θ] x^2

Plugging in your values, that is

y = 0.707x - 0.196x^2

The vertex is at (1.8,0.6)

So, a distance of 1.8 meters will provide the maximum clearance.