A boy whose eye level is 1.3 m from the ground,  spots a balloon moving with the wind in a horizontal level at some height from the ground.  The angle of elevation of the balloon from the eyes of the boy at any instant is 60°. After 2 s,  the angle of elevation becomes is 29√3 m/s, then find the height of the balloon from ground. 

Asked by pdcavita | 19th Nov, 2017, 03:05: PM

Expert Answer:

 
begin mathsize 16px style Let space straight P space be space the space position space of space the space boy
rightwards double arrow AP equals 1.3 space straight m
Let space straight C space and space straight E space be space the space two space positions space of space the space balloon.
Speed space of space the space wind equals 29 square root of 3 space straight m
Distance space travelled space by space the space baloon space in space 2 space secs equals CE equals BD equals 2 cross times 29 square root of 3 equals 58 square root of 3 space straight m
Let space AB equals straight x space straight m space and space BC equals DE equals straight y space straight m
In space triangle ABC comma
tan space 60 degree equals BC over AB rightwards double arrow square root of 3 equals straight y over straight x
rightwards double arrow straight x equals fraction numerator straight y over denominator square root of 3 end fraction space space space space space.... left parenthesis straight i right parenthesis
In space triangle ADE comma
tan space 30 degree equals DE over AD
rightwards double arrow fraction numerator 1 over denominator square root of 3 end fraction equals fraction numerator straight y over denominator straight x plus 58 square root of 3 end fraction rightwards double arrow square root of 3 straight y equals straight x plus 28 square root of 3
rightwards double arrow square root of 3 straight y equals fraction numerator straight y over denominator square root of 3 end fraction plus 28 square root of 3 space space space space space.... left square bracket From space left parenthesis straight i right parenthesis right square bracket
rightwards double arrow square root of 3 straight y equals fraction numerator straight y plus 174 over denominator square root of 3 end fraction rightwards double arrow 3 straight y equals straight y plus 174 rightwards double arrow 2 straight y equals 174 rightwards double arrow straight y equals 87 space straight m
Thus comma space height space of space the space balloon space from space the space ground equals ER equals straight y plus 1.3 equals 87 plus 1.3 equals 88.3 space straight m end style

Answered by Rashmi Khot | 30th Nov, 2017, 10:18: AM