A landscape architect is planning an artificial waterfall in a city park. Water

Question

A landscape architect is planning an artificial waterfall in a city park. Water flowing at 1.67 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 3.20 m high, and from there the water falls into a pool (see figure).
(a) Will the space behind the waterfall be wide enough for a pedestrian walkway? (Assume that the average pedestrian walkway is 1 m wide.)
Yes No    
(b) To sell her plan to the city council, the architect wants to build a model to a scale, which is one-thirteenth actual size. How fast should the water flow in the channel in the model?
m/s

Explanation / Answer

First we need to find out how long it takes for the water to hit the ground:

d = 1/2*g*t^2
so
3.2 = .5*9.8*t^2
t^2 = 0.653
so
t = 0.81 seconds

the water travels 1.67 meters in one second so in .81 second it will travel 1.349 meters

a) if 1 meters are needed for a walkway, then there will be enough space to walk

c) divide everything by 13 and get the new figures:

3.2/13 = 0.24 m and 1.34/13 = 0.10 m

0.24 = .5*9.8*t^2, t =0.221 sec so .10 = r * 0.221 , r = 045 m/s

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