Question

A peacock is sitting on a 19 m long pole, a snake is approaching the hole which is at bottom of the pole, the snake is 27 m away from the hole, if their speeds are same, find the distance from the hole at which the peacock pounces over the snake.

a. 3.4 m

b. 6.8 m

c. 5.9 m

d. 7.3 m

Answer 1

Answer:

b) 6.8

Explanation:

They both have same speed hence if snake moves 'x' then peacock also moves 'x' but diagonally down from the pole...

hence path of peacock , ground, and the pole make a triangle...... with diagonal (Hypotenuse) = x

snake moves 'x' hence distance left =( 27 - x ) which is the base of triangle

and height of the pole is the height of triangle =19.

now, apply pythagoras' theorem----- x^2= (27-x)^2 + 19^2

solve the equation ..... x= 20.18 m

And the distance from the hole at which the peacock pounces over the snake = 27 - 20.18 = 6.8

Answer 2

Given:

Height of pole $\[ = 19\,m\]$

Distance of snake from the pole $\[ = 27m\]$

To Find: The distance from the hole at which the peacock pounces over the snake

Solution:

Consider the given figure below. The peacock is at point A, the snake is at point C and the hole is at point B.

Suppose that the peacock catches the snake at a distance $x$ from the hole.

Then, the snake travelled $(27-x)$ distance (DC) and in the same time, the peacock travelled AD distance.

$\begin{gathered} AD = \sqrt {A{B^2} + B{D^2}} \hfill \\ AD = \sqrt {{{19}^2} + {x^2}} \hfill \\ \end{gathered}$

Suppose this time is $t$ and peacock and snake have the same speed. Then,

$\begin{gathered} \frac{{27 - x}}{t} = \frac{{AD}}{t} \hfill \\ \frac{{27 - x}}{t} = \frac{{\sqrt {{{19}^2} + {x^2}} }}{t} \hfill \\ \left( {27 - x} \right) = \sqrt {{{19}^2} + {x^2}} \hfill \\ \end{gathered}$

Squaring both sides, we have,

$\begin{gathered} {\left( {27 - x} \right)^2} = {19^2} + {x^2} \hfill \\ 729 + {x^2} - 54x = 361 + {x^2} \hfill \\ 368 - 54x = 0 \hfill \\ \end{gathered}$

Thus,

$\begin{gathered} x = \frac{{368}}{{54}} \hfill \\ x = 6.81m \hfill \\ \end{gathered}$

Hence, the peacock catches the snake at a distance $6.81\,m$ from the hole. Thus, the correct option is b. 6.8 m.

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