question

Asked by arindeep.singh | 2nd Oct, 2020, 12:19: PM

Expert Answer:

Question: A straight highway leads to the foot of a tower. a man standing at the top of the tower observes a car at an angle of depression of 30 degree, which is approaching the foot of the tower with a uniform speed. 6 seconds later, the angle of depression of the car is found to be 60 degree. find the time taken by the car to reach the foot of the tower from this point?
Solution:

A s space s h o w n space i n space t h e space f i g u r e comma T h e space c a r space t a k e s space 6 space s e c s space t o space t r a v e l space f r o m space D space t o space C. space L e t space t h e space c a r space t a k e s space t space s e c s space t o space t r a v e l space f r o m space C space t o space t h e space f o o t space o f space t h e space t o w e r space a s space s h o w n space i n space t h e space f i g u r e. S i n c e space t h e space s p e e d space i s space u n i f o r m comma space d i s tan c e space i s space p r o p o r t i o n a l space t o space t i m e. C D space equals space 6 V space a n d space B C equals V t space comma space w h e r e space V space i s space t h e space u n i f o r m space s p e e d. I n space t r i a n g l e space A B D comma space d equals fraction numerator 6 V plus t V over denominator t a n space 60 end fraction equals fraction numerator V over denominator square root of 3 end fraction open parentheses 6 plus t close parentheses... left parenthesis 1 right parenthesis I n space t r i a n g l e space A C B comma space d equals fraction numerator V t over denominator tan space 30 end fraction equals square root of 3 V t... left parenthesis 2 right parenthesis F r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis fraction numerator V over denominator square root of 3 end fraction open parentheses 6 plus t close parentheses equals square root of 3 V t rightwards double arrow 6 plus t equals 3 t rightwards double arrow 2 t equals 6 rightwards double arrow t equals 3 space s e c s


Answered by Renu Varma | 3rd Oct, 2020, 03:43: PM