Q.8 (b) part

Q.8 (b) part at a of 40 heads sharp 90' turn by the Of A af a speed ur 100 starts frcvn instant the is 20 km auu_v. Nies unfil it reaches the glasspane of the returns rhe wall at the same speed. It continues to the car and the wall till the car makes the 90: turn. (a) What is the total distance the fly has during this period ? (b) How many trips has it made between the car and the wall ? Solution : (a' The time taken by the car to cover 20 km 20 km I = —h. The fly moves at a before the turn is 40 km/h 2 constant speed of 100 km/h during this time. Hence the km 1 total distance coverd by it is 100 —x — h = 50 km. (b) Suppose the car is at a distance x away (at A) when the fly is at the wall (at O). The fly hits the glasspane at B, taking a time t. Then and rhus, AB = (40 knvh)t, 0B = (100 km/h)t. x=AB+OB = (140 knv'h)t 5

Dear student,

(b)

Suppose the car is at A which is x km away when the fly is at the wall, O. The fly hits the glass pane at B, taking a time t we have,

AB = 40t

OB = 100t

Therefore, x = AB + OB = 140t

=> t = x/140

And, OB = (5/7)x

The fly returns to the wall and during this period the car moves through distance BC. The time taken by the fly in this return path is = (5/7)x/100 = x/140

Thus, BC = (time)(speed of car) = (x/140)(40) = (2/7)x

And, OC = OB – BC = (5/7)x – (2/7)x = (3/7)x

If at the beginning of the round trip (wall to car and back) the car is at a distance x away when the next trip again begins.

The distance of the car at the beginning of the 1^st trip is = 20 km

The distance of the car at the beginning of the 2^nd trip is = (3/7)(20) km

The distance of the car at the beginning of the 3^rd trip is = (3/7)²(20) km

The distance of the car at the beginning of the 4^th trip is = (3/7)³(20) km

The distance of the car at the beginning of the n^th trip is = (3/7)^n-1(20) km

The trips will continue till the car reaches the turn that is 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 car takes the turn.

Regards