Question

A car is moving at a constant speed of $40km/h$ along a straight road which heads towards a large vertical wall and makes sharp ${90}^o$ turn by side of the wall. A fly flying at a constant speed of $100km/h$, starts from the wall towards the car at an instant when the car is $20km$ away, flies until it reaches the glass pane 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 ${90}^o$ turn. How many trips has it made between the car and the wall?

• A. $50$
• B. Infinite
• C. $66$
• D. $150$

Answer 1

The correct option is B Infinite

Time taken by flying from $O$ to $B$ is

$t_1=\frac{20}{140}$

and $AB=\frac{20}{140}\times 40=\frac{2}{7}\times 20OB=\frac{5}{7}\times 20$

time taken by flying from $B$ to $O$ is $t_2=\frac{5\times 20}{7\times 100}=\frac{1}{7}$ and $BC=\frac{1}{7}\times 40=\frac{2}{7}\times 20$ and $OC=\frac{3}{7}\times 20$

In first trip distance reduced to $\frac{3}{7}th$ of total distance at $n^{th}$ trip displacement of car from wall ${\left(\frac{3}{7}\right)}^n$

If displacement is zero then $n⟶\infty$