Homework Help: calculus

Posted by ibo on Wednesday, September 29, 2010 at 2:52pm.

A rocket rises vertically from a point on the ground that is 100m from an observer at ground level. The observer notes that the angle of elevation is increasing at a rate of 12∘per second when the angle of elevation is 60∘. Find the speed of the rocket at that instant. Hint: remember to use radians.

calculus - Reiny, Wednesday, September 29, 2010 at 4:49pm
make a diagram.
you should have a right-angled triangle, where the angle of elevation is Ų, the adjacent is 100 and the opposite is h, the height of the rocket.

tanŲ = h/100
h = 100tanŲ
dh/dt = 100sec^2 Ų (dŲ/dt)

when Ų = 60° or π/3 rad
dŲ/dt = 12°/sec or 12π/180 rad/sec = π/15 rad/sec

sub into the dh/dt equation and you are done

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