Question

A lotus flower blooming in a lake the lower is 1/2 metres above the surface of the lake in the Western when blows the flower droops at a distance of 2 m from the base find the depth of the lake.

Answer 1

Solution:

Possibility 1.

Distance between surface of water to the tip of lotus=$\frac{1}{2}$

As, when  Western wind blows the flower droops at a distance of 2 m from the base.

To, find , the depth of the lake

Drawn, the image of the statement described in the problem.

In Right Δ CAB, right angled at A

Using Pythagoras theorem

→BC²=CA² +AB²

→BC²=2² + $(\frac{1}{2})^2$→→Considering the flower has negligible length.

→BC²= 4 +$\frac{1}{4}$

→→BC²= $\frac{17}{4}$

→→→BC =

             $\frac{\sqrt{17}}{2}$ meter

=

$\frac{4.12}{2}=2.06$ meter(approx)

2. Possibility 2

If flower droops at a distance of 2 meter from the surface of base, considering the length of flower as negligible,

Total Distance between surface of water to the base of water

= 2 + $\frac{1}{2}$

= $\frac{5}{2}$ meter

Image of this possibility is also Attatched below.

Why, i have considered possibility 2, because in Possibility 1 ,the depth of water lake is slanted distance , which is hypotenuse of Right triangle, which can't be the actual distance between surface of water to base of water.