Find the distance at which the peacock will catch the snake

1. Mar 23, 2013

gnrlies00

1. The problem statement, all variables and given/known data

A peacock perched on top of a 12m high tree spots a snake moving towards its hole at the base of the tree from a distance equal to thrice the height of the tree. The peacock flies towards the snake in a straight line and they move at the same speed. At what distance from the base of the tree will the peacock catch the snake?

2. Relevant equations

1)equation of line
2) Pythagoras theorem

3. The attempt at a solution

I used the equation of the line and tried to find the slope

m= $\frac{y-yo}{x-xo}$

$\Rightarrow$ m=$\frac{0-12}{36-0}$

$\Rightarrow$ m=$\frac{-12}{36}$ = -0.33

and then tried substituting this slope in the other equation of line in which the peacock catches the snake.

But I think this is wrong

Last edited: Mar 23, 2013
2. Mar 23, 2013

Staff: Mentor

That slope would require a stationary snake.

Did you draw a sketch? This will help a lot.

3. Mar 23, 2013

gnrlies00

yes, I have drawn the sketch.
and I know that this problem is very easy, but I can't figure out how to go about the solution.

Please give me some hints.

4. Mar 23, 2013

Staff: Mentor

Mark the position where they hit each other, and define some variable expressing its position. Calculate the distance both animals travel, and use that they have to be equal. This allows to get the value of your variiable.

5. Mar 23, 2013

gnrlies00

the distance are equal
$\Rightarrow$ 36-S1=12-P1
$\Rightarrow$ S1-P1=24

Is this correct???
If yes, then how do I get the second equation?

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Last edited: Mar 23, 2013
6. Mar 23, 2013

Staff: Mentor

What is 12-P11?
You'll need Pythagoras there. And there should be no P11 in your equation.

7. Mar 24, 2013

gnrlies00

P1 is the y-coordinate where the peacock catches the snake,
in this case P1=0

therefore

36-S1=12-0
S1=24

But on the book they have given the answer as 16 meters.

8. Mar 24, 2013

Sunil Simha

Since the time taken to reach the point by both and their speeds are the same, just equate the distances that they have traveled.

9. Mar 24, 2013

gnrlies00

I did that in my previous post and I got the answer 24 meters, but the correct answer is required to be 16 meters.

10. Mar 24, 2013

Sunil Simha

the answer does come to be 16 m the correct equation is
$\sqrt{12^2 + s_1^2} = 36-s_1$

11. Mar 24, 2013

gnrlies00

Thanks guys!!