A cylindrical water tank that is open to the atmosphere at the top is filled wit

Question

A cylindrical water tank that is open to the atmosphere at the top is filled with water to depth of 3.5m and is situated on the roof of a building that is 50.0 meters tall. A small leak develops at the bottom of the water tank3m below the surface of the water, with the water emerging horizontally, as shown in the schematic. The hole in the tank is located 50.5 meters from the ground level. y"x"a.Using your knowledge of fluid dynamics determine the speed of the water emerging from the small hole.b.Determine the time it takes for the water to hit the ground once it emerges from the hole in the tank. If you were not capable of doing part a) assume the water speed of the water as it emerges from the hole is 7.0m/s. (this is not the correct answer to part (a)for those who were able to do it). c.How far from the base of the building (i.e. along the x axis) does the water hit the ground? d.What is the velocity (magnitude and direction) of the water just before it hits the ground? Express the angle in degrees relative to the positive x axis.e.If the velocity that the water emerges from the tank is doubled, does this time it takes for it to reach the ground change? Explain your answer briefly. If no explanation is provided no credit will be given.

Explanation / Answer

Here,

a) depth of water at the hope , d = 3 m

speed of water flowing out of hole = sqrt(2 * g * d)

speed of water flowing out of hole = sqrt(2 * 9.8 * 3)

speed of water flowing out of hole = 7.67 m/s

b)

time taken for water to hit ground = sqrt( 2* h/g)

time taken for water to hit ground = sqrt(2 * 50.5/9.8)

time taken for water to hit ground = 3.21 s

c)

distance from the base of building = 3.21 * 7.67 m

distance from the base of building = 24.6 m

d)

for the final velocity

vy = 3.21 * 9.8 = 31.5 m/s

magnitude of velocity = sqrt(31.5^2 + 7.67^2)

magnitude of velocity = 32.4 m/s

direction of velocity = arctan(31.5/7.67)

direction of velocity = 76.5 degree

the direction of velocity is 76.5 degree below the horizontal

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