SOLUTION: a balloon is rising at the rate of 12 feet/seconds and at the same time is being blown horizontally by a wind at 18 feet/seconds. find the angle its path makes with the vertical an

Algebra ->  Finance -> SOLUTION: a balloon is rising at the rate of 12 feet/seconds and at the same time is being blown horizontally by a wind at 18 feet/seconds. find the angle its path makes with the vertical an      Log On


   

Question 1034319: a balloon is rising at the rate of 12 feet/seconds and at the same time is being blown horizontally by a wind at 18 feet/seconds. find the angle its path makes with the vertical and determine its actual velocity.
Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) About Me  (Show Source):
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a balloon is rising at the rate of 12 feet/seconds and at the same time is being blown horizontally by a wind at 18 feet/seconds. find the angle its path makes with the vertical and determine its actual velocity.
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tan of the angle with vertical = 18/12
angle =~ 56.3 degs
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speed is the hypotenuse of the right triangle with sides of 12 & 18

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
if you draw this and look at the vector, the hypotenuse of the triangle, the resultant, is the square root of (12^2+18^2)=sqrt (468)=21.63 ft/sec
The angle with the vertical is the tangent (18/12)=1.5
tan(-1) (1.5)=56.31 degrees, which is the angle with the vertical. This makes intuitive sense, since the balloon is rising less quickly than it is being moved horizontally, and therefore has an angle with the vertical greater than 45 degrees.