SOLUTION: Bob is taking a hot air balloon ride. Jenny is standing on level ground, 100 feet from the balloon launchpad, capturing the moment on Video. At one instant, Jenny has to tile the c

Algebra ->  Trigonometry-basics -> SOLUTION: Bob is taking a hot air balloon ride. Jenny is standing on level ground, 100 feet from the balloon launchpad, capturing the moment on Video. At one instant, Jenny has to tile the c      Log On


   

Question 1077780: Bob is taking a hot air balloon ride. Jenny is standing on level ground, 100 feet from the balloon launchpad, capturing the moment on Video. At one instant, Jenny has to tile the camera on its tripod at an angle of elevation of 32 degree to keep Bob in frame. One minute later, she has tilted the camera to an angle of elevation of 76 degree. What is Bob's vertical speed in mph?
Please help me to solve this. Thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h%5B1%5D+ = the baloon's height in feet when
Jenny has the camera at a +32+ degree angle
to the horizontal
Let +h%5B2%5D+ = the baloon's height in feet when
Jenny has the camera at a +76+ degree angle
to the horizontal
--------------------------------------------
Jenny is +100+ ft from the point which is directly
below the baloon, so I can say:
+h%5B1%5D+=+100%2Atan%28+32+%29+
+h%5B1%5D+=+100%2A.62487+
+h%5B1%5D+=+62.487+ ft
and, also
+h%5B2%5D+=+100%2Atan%28+76+%29+
+h%5B2%5D+=+100%2A4.01078+
+h%5B2%5D+=+401.078+
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While 1 minute has elapsed, Bob has traveled:
+h%5B2%5D+=+h%5B1%5D+=+401.078+-+62.487+
+h%5B2%5D+-+h%5B1%5D+=+338.591+
----------------------------
Convert +1+ min to hours
+1%2F60+ hr
-------------------
Convert +338.591+ ft to miles
+338.591+%2F+5280+=+.06413+ miles
-----------------------------------
[ rate ] = [ distance ] / [ time ]
Bob's vertical speed is:
+.06413+%2F+%28+1%2F60+%29+=+3.848+ miles/hr
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Check the math & get another opinion if needed