Question

Q . An ant is at point A of a segment AB, having length 12. The ant moves as follows:
First it moves 3 units towards B, then moves 2 units towards A: again moves 3 units
towards B, then moves 2 units towards A, and so on. Find the total distance traveled by the ant, when it reaches point B for the first time.

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Answer 1

Answer:

Let us move the mirror to the point Q. Ant is covering a distance of PQ(=60cm) in 2×60s. ∠PQM=30  0

From similar triangle we get, ∠MQ  1   P  1  =30  0

Since ∠PQP  1 ​   =60  0 ,

we get PQ=P  1 ​

Q  1 =PP  1  =60cm

Now,

PP  1  =60cm and

QQ  1  =0cm.  

So, the rate at which the distance between ant and its image change is 2×60 60 cm/s=0.5cm/s

Answer 2

the distance travelled by the ant when it reaches point B for first time is 60cm.