Asked by Karen

A gallon rises at the rate of 8 feet per second from a point on the ground 12 feet from an observer. To 2 decimal places in radians per second, find the rate of change of the angle of elevation when the ball on is 9 feet above the ground. Type your answer in the space bellow. If your answer is a number less than 1, place a leading "0" before the decimal point (ex:0.35)
Answered by Reiny
Make your sketch. (What is rising, a gallon, a ball or a balloon ????)

let the height of "whatever is rising" be y ft
let the angle of elevation be Ø
tanØ = y/12
y = 12 tanØ
dy/dt = 12sec^2 Ø dØ/dt

in your sketch, let y = 9
then h^2 = 12^2 + 9^2 = 225
h = 15
then cosØ = 12/15 = 4/5
secØ = 5/4
sec^2 Ø = 25/16

now you got all your values to put into
dy/dt = 12sec^2 Ø dØ/dt
Answered by ALICE Urgentttt
Yes I'm sorry, i meant to type "balloon". I'm still a little confused, can you give me the exact number that is the answer so I can better understand please?
Answered by Reiny
Giving you the "exact" number, will not help you understand it, the solution I gave you
will help you understand it.
Answered by Karen
ok but I need to finish with the exercise with the answer but I don't understand. Can you finish with my question please?
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