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CBSE Class 9 Answered

Two points A and B are located on the floor of a room 30cm and 20cm away from a wall. The distance between the points parallel to the wall is 50cm. An insect is at moving on the floor at 5cm/s. It has to first reach a point C on the wall and then reach B such that AC and BC make equal angles with Normal to the wall at C. The time taken for this  motion will be
Asked by rajesh kumar | 21 Oct, 2022, 08:15: PM
Expert Answer
Figure shows the two points A and B that are at distances 30 cm and 20 cm respectively.
 
Distance between A and B parallel to wall is 50 cm .
 
If the insect moves from A , reaches point C then moves towards B. in straight line path as shown in figure.
 
Each straight line path makes equal angle with the vertical line to the wall drawn at C .
 
We can see that using basic geometry , straight line paths AC and CB also makes equal angle with wall.
 
Let us consider two points D and E at wall exactly opposite to A and B respectively as shown in figure.
 
begin mathsize 14px style angle end style ACD = begin mathsize 14px style angle end styleBCE as explained above .
Hence begin mathsize 14px style increment end style ACD  and begin mathsize 14px style increment end styleBCE are similar triangles
 
DC / EC = AD / BE  = 30/20
 
also we have , DC+CE = 50 cm
 
Hence from above two expressions, we get , DC = 30 cm and BE = 20 cm
 
AC = 30√2 cm  ,  BC = 20√2 cm
 
Time taken by insect to travel along AC and then CB is calculated as
 
time = distance / speed =  [ ( 30 + 20 ) √2 ] / 5 = 10 √2 s  = 14.1 s
Answered by Thiyagarajan K | 21 Oct, 2022, 11:33: PM
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