Question
A balloon, 50 feet from an observer is rising at 20 ft/sec. At 5 sec after lift off,
a)how fast is the distance between the observer and the balloon changing?
b)How fast is the angle of elevation changing.
I just need to know what formals to use. I know the first part requires tan = x/50, but I'm not sure what to do next, and what to do for B.
a)how fast is the distance between the observer and the balloon changing?
b)How fast is the angle of elevation changing.
I just need to know what formals to use. I know the first part requires tan = x/50, but I'm not sure what to do next, and what to do for B.
Answers
as you say,
tanθ = x/50
so, sec^2 θ dθ/dt = 1/50 dx/dt
You know x at t=5, and you know dx/dt=20, so you can find θ.
The distance z is given by
z^2 = 50^2 + x^2
z dz/dt = x dx/dt
so, find z at t=5 and plug in the numbers.
tanθ = x/50
so, sec^2 θ dθ/dt = 1/50 dx/dt
You know x at t=5, and you know dx/dt=20, so you can find θ.
The distance z is given by
z^2 = 50^2 + x^2
z dz/dt = x dx/dt
so, find z at t=5 and plug in the numbers.
Thanks for your help, but sorry, I'm still kinda confused.
I'm not sure how to find x. Do I need it to solve for z.
z^2 = 50 ^2 + x^2
Sorry if this is a silly question
I'm not sure how to find x. Do I need it to solve for z.
z^2 = 50 ^2 + x^2
Sorry if this is a silly question
well, of course. (it is kind of a silly question) You know after 5 seconds the balloon has gone up 5*50 = 250 feet.
Now you know x and you can get z.
Now you know x and you can get z.
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