# Car and the fly!

## Homework Statement

A car moving at constant speed of 40 km/h in a straight road which heads towards a wall makes a 900 (90 degree) turn by the side of the wall. A fly flying at constant speed 100km/h starts from wall till car and when it reaches the car turns back and flies towards wall at same speed (100 km/h). This procedure starts when the car is 20 km away from the wall. The fly continues its journey till the car takes the 90 - degree turn.
So how many trips has the fly made between the car and wall?

## Homework Equations

$$distance = speed * time$$

## The Attempt at a Solution

[PLAIN]http://img294.imageshack.us/img294/2922/suma.png [Broken]

A is the initial position of car. B is the position where the fly first meets the car. O is the wall.
So let x = 20km be distance from car to wall.
Let t be time taken for car to reach from A to B
Now

AB = 40t
OB = 100t
but,
x = AB + OB
t = x/140

therefore
$$OB = \frac{5x}{7}$$

This is all that I got...
When I checked answers it says infinite....
I just dont get it..

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Well, the fly's velocity is initially opposite that of the car, so you've got to make one of them negative. When the fly goes back toward the wall then both velocities are the same sign. That will change your expression a bit. Sounds like you're supposed to get a diverging geometric series, if the answer is infinite.

I didn't quite get the:
x = x/140
and the
OB = 5x/7

But the reason the fly made infinite trips, i guess, is that the closer the car gets to the wall, the quicker the fly makes a trip. And finally when the car reaches the wall, the distance of the fly's trip is 0, therefore at that moment it will make infinite number of trips.

Hope I didn't just lie to you :)

kuruman
Homework Helper
Gold Member
Do yo need to find the total distance the fly flies or are you looking for the number of back and forth trips?

I didn't quite get the:
x = x/140
its like this
t = x/140

I didn't quite get the:
OB = 5x/7
substituting t
OB = 100 t = 100x/140 = 5x/7

But the reason the fly made infinite trips, i guess, is that the closer the car gets to the wall, the quicker the fly makes a trip. And finally when the car reaches the wall, the distance of the fly's trip is 0, therefore at that moment it will make infinite number of trips.
But .... I feel this may be wrong. (no offense)

Do yo need to find the total distance the fly flies or are you looking for the number of back and forth trips?
I need to find the number of back and forth trips.

Well, the fly's velocity is initially opposite that of the car, so you've got to make one of them negative. When the fly goes back toward the wall then both velocities are the same sign. That will change your expression a bit. Sounds like you're supposed to get a diverging geometric series, if the answer is infinite.
you are considering velocity.... instead I have taken it in terms of speed according to the question(hope I did the right thing)

And about the diverging geometric series......... could you please tell me what it is (I just know geometric progression)