A landscape architect is planning an artificial waterfall in

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?

Solution

a) time take by water to travel 3.55m vertically.

using h = ut + at^2 /2

3.55 = 0 + 9.81t^2 /2 (initial vertical component of velocity is zero)

t = 0.851 sec

distance traveled in horizontal = vt = 1.70 x 0.851 = 1.45 m

yes, it is more than 1m.

b) now h \' = h/14 = 3.55/14 = 0.254 m

same procedure, 0.254 = 0*t + 9.81t^2 /2

t = 0.227 sec

and new d\' = 1.45/14 = 0.104 m

and d\' = v\' t \'

0.104 = v( 0.227)

v = 0.456 m/s