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 1.70 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 3.55 m high, and from there the water falls into a pool.

(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 or no)

(b) To sell her plan to the city council, the architect wants to build a model to a scale, which is one-fourteenth actual size. How fast should the water flow in the channel in the model?

Explanation / Answer

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

d = 1/2*g*t^2 so 3.55 = 0.5*9.8*t^2 and t^2 = 0.7245 so t = 0.85 seconds

the water travels 1.7 meters in one second so in 0.85 second it will travel 1.45 meters

if 1 meters are needed for a walkway, then there will be enough space.

b) divide everything by 14 and get the new figures:

3.55/14 = 0.254 m and 1.45/14 = 0.104 m

0.254 = 0.5*9.8*t^2

t =0.228 sec

so 0.104 = r *0.228

r = 0.456m/s

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