You hold a hose 45 degrees to the horizontal and at a height of 1 m from the floor. The water reaches a maximum distance of 10 m from where you are standing. Now you place your thumb over the end of the hose to occlude the opening by 80%, which in turn reduces the flow rate by 50%. Even though less fluid emerges the water travels further. How far does the water travel with your thumb over the end of the hose? Find the amount by which the hose must be occluded in order for the water to travel twice as far.

Answer 1

convert this into a projectile problem.

First solve for velocity of projectile needed to reach ground at 10 meters when fired at 45 deg from height of 1 m
Call that V1

Now find V2, the new velocity
Q2 = .5 Q1 = .5 * V1 * A1
and Q2 = V2 A2 so
V2 = .5 V1 (A1/A2) = .5*(1/.2) * V1 = 2.5 V1