Another projectile motion question (1 Viewer)

[Trebla]

Hi guys,
I need just quick help with a part of this question:

Prove that the range on a horizontal plane of a particle projected upwards at an angle A to the plane with velocity V metres per second is (V²sin 2A)/g metres
A garden sprinkler sprays water symmetrically about its vertical axis at a constant speed of V metres per second. The inital direction of the spray varies continuously between angles of 15 and 60 degrees to the horizontal.
Prove that, from a fixed position O on level ground, the sprinkler will wet the surface of an annular region with centre O and with internal and external radii V²/2g and V²/g metres respectively.
*Deduce that, by locating the sprinkler appropriately relative to a rectangular garden bed of size 6 metres by 3 metres, the entire may be watered provided that (V²/2g) ≥ 1 + √(7)

I got everything except the * part, in which I am clueless on how to approach....
Thanks...

 

[haque]

draw two concentric circles and draw the rectangle in the annular region between the circles(rectangle side touching the circumference of the circle). construct a line from O to an edge of the rectangle(call it OX) and a perpendicular to the furthest edge of the rectangle(call the furthest edge XY)
thus let this point on furthest edge be D
OD^2=OX^2-XD^2 but entire bed will be wet if OD>=3+V^2/2g
(V^2/g)^2-9>=(3+V^2/2g)^2
solving gives V^2/2g>= root 7 +1