a man, walking due north, observes that the elevation of a balloon, which is due east of him, and is sailing towards the north west, is then 60 after he has walked 400 m the balloon is vertically over his head, find its height supposing it to have always remained the same..Ans... 692.8 m

dear student,

 Let the height of the balloon be h. So, initially, the distance between the man and the balloon is h/ root3 as shown in the figure. (This diagram is in the plane perpendicular to the ground.)

Next, when he has walked 400m in North direction, the balloon is over his head. The balloon travels in North-West direction, and the motion is eplained in the next diagram. (This is in a plane parallel to the ground.)

As it is clear, ABC is a right angled isosceles triangle, with AB = BC, as angle ACB is 45 degrees(North of West) and AB is perpendicular to BC(North and West).

So, we get,

h/root3 = 400, 

or, h =  m

Hence the ballon is at a height of   m (or 692.8 m) 

 BEST OF LUCK..!!!!

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