Question
A car is moving with a constant speed of 30km/hr along a straight line towards a vertical wall. A fly flying at a constant speed of 60km/hr starts from a wall towards the car when it is 90km away from the wall. The fly flies till it reaches the glass pane of car and then returns to wall at the same speed. After touching the wall again it flies towards car. Fly continues its motion till car just touches the wall. Find the total distance travelled by fly. How many trips the fly will make?
Solution
Speed of car, v = 30 km/hr
Distance of wall, d= 90 km
Time taken by car to reach the wall is,
Fly moves back and forth between car and the wall with constant speed 60km/hr.
Therefore, distance travelled by fly is,
S = ut
= 60 x 3
= 180 km
To find: The distance travelled by the fly in it's one complete trip.
Consider, initially when the fly is flying from the wall towards the car, it is at a distance D from the wall.
Speed at which the car is approaching the fly = 30 km/hr
Speed at which the fly is flying towards the car = 60 km/hr
Let both car and fly meet after time t1.
Thus distance travelled by car and fly respectively is,
The fly will return to the wall.
Let t2 be the time taken by fly to come back to the wall.
In time t2, the distance moved by the car towards the fly is,
Distance travelled by the car after completing 1 trip is,
d =
When fly completes one trip, distance of car from the wall is,
Thus, if at the beginning of motion, the car is at a distance D from the wall, then after completion of one trip of fly, it will be at a distance one-third of initial distance i.e. 1/3 D from the wall.
Thus, the distance of car from wall after n trips will be
Therefore, the fly will make infinitely many trips.
