3. 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 is
20 km away, flies until it reaches the glasspane of the
car and returns to the wall at the same speed. It continues
to fly between the car and the wall till the car makes the
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 ?
Answers
Answer:
Solution :
(a) The time taken by the car to cover 20 km
before the turn is 201un1 h. The fly moves at a 40 km/h - 2
constant speed of 100 km/h during this time. Hence the
total distance coverd by it is 100 —khm x h = 50 km.
(b) Suppose the car is at a distance x away (at A) when
the fly is at the wall (at 0). The fly hits the glasspane
at B, taking a time t. Then
AB = (40 km/h)t,
and OB = (100 km/h)t.
Thus, x =AB + OB
= (140 km/h)t
or, t - 140 km/h °B=
5
7 x.
The fly returns to the wall and during this period the
car moves the distance BC. The time taken by the fly
in this return path is
5x/7
100 km/h)- 140 km/h •
ru-, = 40 x 2
140 = x
oc = OB - BC= x.
Thus,
or,
If at the beginning of the round trip (wall to the car and
back) the car is at a distance x away, it is 17 x away
when the next trip again starts.
Distance of the. car at the beginning of the 1st
trip = 20 km.
Distance of the car at the beginning of the 2nd trip
= -
3 x 20 km. 7
Distance of the car at the beginning of the 3rd trip
2
=I 10 )X 2 km. 7
Distance of the car at the beginning of the 4th trip
=131 x20 km. 7
Distance of the car at the beginning of the nth trip
n
(
1) X 20 km. 7
Trips will go on till the car reaches the turn that is the
distance reduces to zero. This will be the case when n
becomes infinity. Hence the fly makes an infinite
number of trips before the car takes the turn.