15. 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 = 2.35 m high, and from there it will fall into a pool (see Figure on
the right). (a) Will the space behind the waterfall be wide enough for a pedestrian
walkway? (b) To sell her plan to the city council, the architect wants to build a
model to standard scale, which is onetwelfth
actual size. How fast should the
water flow in the channel in the model?
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 =2.35 m high . and from there it will fall into a pool ( Fig . P4.18) (a) will the space behind the waterfall be wide enough for a pedestrian walkway? (b) to sell her plan to the city council, the architect wants to build a model to standard scale, which is one -twelfth actual size . how fast should the water flow in the channel in the model ?
I want koown answer
it will take 0.69 seconds for the water to fall 2.35 meters.
At 1.70 m/s, the water will be 1.177 m from the wall when it hits.
So, how wide is your walk?
More important, how tall do you expect the pedestrians to be? The water must be far enough from the wall not to hit the tallest on the head.
I want known answer
Please
Without the figure...
It sounds as if you need to compute the velocityh of the water coming out, then determine the distance it travels horizonally.
244004
To determine whether the space behind the waterfall will be wide enough for a pedestrian walkway, we need to consider the projectile motion of the falling water.
(a) First, let's find the time it takes for the water to fall from the top of the vertical wall to the pool below. We can use the equation:
h = (1/2) * g * t^2
where h is the height of the wall (2.35 m) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Rearranging the equation, we get:
t = sqrt(2h/g)
Substituting the values, we find:
t = sqrt(2 * 2.35 / 9.8) ≈ 0.677 seconds
Now, let's find the horizontal distance the water travels during this time. We can use the equation:
d = v * t
where v is the horizontal velocity of the water (given as 1.70 m/s) and t is the time calculated above. Substituting the values, we get:
d = 1.70 * 0.677 ≈ 1.152 meters
So, the horizontal distance the water travels is approximately 1.152 meters.
To determine if the space behind the waterfall will be wide enough for a pedestrian walkway, we need to compare this distance with the desired width of the walkway.
(b) The architect wants to build a model to a standard scale of one-twelfth the actual size. This means that linear dimensions, such as height and width, are reduced to 1/12 of their actual measurements.
To determine how fast the water should flow in the model, we need to scale down the velocity as well. Since the linear dimensions are reduced by a factor of 1/12, the time it takes for the water to fall will also be reduced by the same factor.
Therefore, the speed of the water in the model's channel should be 1/12 of the actual speed.
So, the water should flow at (1.70 m/s) / 12 ≈ 0.142 m/s in the model.
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