A garden hose

Task number: 506

We want to splash as high as possible on a vertical wall (which is situated at a horizontal distance d from the hose’s nozzle) with a jet of water flowing from a garden hose with an initial speed v0.

a) What elevation angle α do we need to choose?

b) At what height h does the water splash on the wall?

c) At what angle ψ does the water hit the wall? Determine the angle (from the horizontal) of the instantaneous velocity vector at the moment of the hit.

Disregard the air resistance.

Solve for these values: v0 = 15 m·s-1, d = 10 m.

  • Analysis

    We want to determine the elevation angle α at which we have to aim the hose so that the water splashes as high as possible. First we have to express how the height of the splash h depends on the angle α. Then we can find the maximum of the function h(α).

    Beware of the idea that the maximum height of the splash on the wall will correspond to the maximum height of the throw for a given angle α. Realize that the distance to the wall is fixed. Draw the different possible situations.

  • Hint 1 for a): picture of the situation, type of motion

    Draw a picture of the situation. What kind of motion is it? How do the x-component and y-component of the speed of the water change with time? How do the x-component and y-component of the coordinates change?


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