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A car is moving at a constant speed of 40 km/h along a straight road which heads towards a large vertical wall and makes a sharp 90° turn by the side of the wall. A fly flying at a constant speed of 100 km/h, starts from the wall towards the car at an instant when the car makes is 20 km away, flies until it reaches the glasspane of the car and returns to the wall at same speed. It continues to fly between the car and wall till the car makes 90° turn. (a) What is the total distance the fly has travelled during this period? (b) How many trips has it made between the car and the wall?

2 years ago

(a) First, calculate the time taken by the car to travel the distance of 20 km before the turn.Using the value of the time taken in the above case and also the speed of the car as 100 km/h, calculate the total distance covered.

(b) Suppose the car is at a distance say x km away from the wall at point A when the fly is at the wall (point O).

The fly hits the glass pane at point B, taking time t, then we have

AB − (40 km/hr)t and OB − (100 km/hr)t

→ x = AB + OB − (140 km/hr) t

The fly now returns to the wall and during the time the car moves the distance BC.

The time taken by the fly in the return path is given as

If at the start of the round trip the car is at a distance x away than it is [93/70x] away when the next trip again begins.

Distance of the car at the start of the 1st trip = 20 km

→ Distance of the car at the start of the 2nd trip = (3/7) × 20 km

→ Distance of the car at the start of the 3rd trip = (3/7)2 × 20 km

→ Distance of the car at the start of the nth trip = (3/7)n-1 × 20 km

Trips will continue till the car reaches the turn where the distance reduces to zero.

This will be the case when n becomes infinity.

Thus, the fly makes an infinite number of trips before the turn.

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