Question about a horizontal stream of water and its speed?

Question

A horizontal stream of water leaves an opening in the side of a tank filled with water to a height of 4.0 m. If the opening is 1.0 m above the ground, find a.) speed of water through the opening and b.) horizontal distance from the base of the tank where water will strike the ground.Assume the stream of water behaves like a projectile thrown horizontally.

Answer 1

a) Conservation of Energy: Gravitation Potential Energy of water is converted into the Kinetic Energy of water leaving the tank horizontally. Note that the height (distance) of water falling down the tank is 3 meters, not 4.

Conservation of Energy formula: mgh = (1/2)mv²

Isolating for v, we'll have:

v = sqrt (2gh)

v = sqrt [(2(9.8)(3)]

v = 7.668 m/s

b) The "free-fall" time of water hitting the ground (vertical distance) is the SAME time as the water hitting the ground horizontally (away from the base).

Free-Fall formula: h = (1/2)gt²

1 = 0.5(9.8)t²

t = 0.452 s

Horizontal Distance formula: d = vt

d = 7.668(0.452)

d = 3.464 m

* To be accurate, the numbers were not rounded off until the last step. *