The head of water on a \(50 \mathrm{~mm}\) diameter smooth nozzle is \(3 \mathrm{~m}\). If the nozzle is directed upward at angles of

(a) \(30^{\circ}\),

(b) \(45^{\circ}\),

(c) \(60^{\circ}\),

(d) \(90^{\circ}\), how high above the nozzle will the jet rise, and how far from the nozzle will the jet pass through the horizontal plane in which the nozzle lies? What is the diameter of the jet at the top of the trajectory?