Question

a water tank on the ground with water upto a height of 20m has a small orifice in its wall at a distance 10m below the surface level of water then the horizontal distance from the hole at which the water touches the ground is​

Answer 1

Explanation:

Velocity of efflux at point D =

2gD

Time taken to reach the ground =

g

2(H−D)

So horizontal range = velocity × time =

2gD

×

g

2(H−D)

So range of the water stream X=2

D(H−D)

Hope it helped you

Thank You

Answer 2

Answer:

The required horizontal distance is 19.99m

Explanation:

Given that,

Height of water in the tank is 20m

$= > H=20m$

It has a smalll orifice at a depth of 10m fromthe surface of water.Hence,the height of orifice above the ground is

$H _{g}=20 - 10 = 10m$

To solve this problem,we shall use Toricelli's theorem.It states that,"The velocity of efflux of a liquid from a certain height is equal to the velocity of a freely falling body from that height".

Now according to Toricelli's Theorem,The velocity of efflux is

$v = \sqrt{ {2H _{g} } \times {g} } \\ = \sqrt{2 \times 10 \times 9.8} \\ = 14ms {}^{ - 1}$

The time taken by water to reach ground is

$t = \sqrt{ \frac{2H _{g}}{g} } \\ = \sqrt{ \frac{2 \times 10}{9.8} } = 1.42 \: s$

The horizontal distance is product of velocity and time.Therefore,

$x = v \times t \\ = 14 \times 1.42 = 19.99 \: m$

Therefore,the required horizontal distance is 19.99m

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