2. You hold a hose at 45 degree to the horizontal and at a height of 1 m from th

Question

2. You hold a hose at 45 degree 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? a) How far does the water travel with your thumb over the end of the hose (assuming the height and angle remain the same)? b) Assume the flow rate (as a percentage of original flow rate) can given by

Explanation / Answer

Time of flight t = 2vy/g
Distance = vx*t = 2vx*vy/g
We must maximize vx*vy as a function of launch velocity v.
vx = vcos?, vy=vsin?
Thus we must maximize sin?cos?. At the maximum, the derivative of sin?cos? = 0. From the ref, the derivative = cos(2?). Thus cos(2?) = 0, 2? = 90 deg, ? = 45 deg.

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