A hot air balloon is precariously tied with a taut rope to an anchor point P. Be
ID: 106903 • Letter: A
Question
A hot air balloon is precariously tied with a taut rope to an anchor point P. Because of steady wind, the balloon lies 5m west and 1m north of a point directly above P. A surveyor positioned 2m east, 1m north and 3m below P observes that the anchor rope makes an angle of 150 degree with her line of sight to P. Suddenly the rope slips and the balloon rises vertically z metres (z > 0). The surveyor checks and finds that-coincidentally-the anchor line still makes an angle of 150 degree to her line of sight to P. Find z.Explanation / Answer
The specific point at which the balloon is tied=P
Initial position of balloon=5m west and 1m north
Position made by surveyor=2m east and 1m north and 3m below P
Angle made by the rope=150 degree
Now the rope slips vertically at z meters and the surveyor finds that still the balloon makes 150degree.
150degree is generally considered as an obtuse angle as it is above 90degree.
When the balloon is said to drop from its normal position still it remains in 150degree in ths sense,it gives the mirror image of the angle.
From 2m east and 1m north and 3m below P the point z would have reached the position in between south and east and z would approximately be equal to 6m (3in upward direction and 3m in lower direction between south and east).
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