I'd do this problem a completely different way. I'm going to call the angle 'a.'
Notice that 132 is constant, don't need a y variable.
I solve for 'a' so we can take a derivative here and find .
Then since we know , the rest is straightforward.
A camera mounted 132ft above the ground is videotaping a racecar moving at 264ft/sec. How fast will the camera angle be changing when the car is right in front of you? a half second later?
">" is the angle
tan>=y/x and dtan>/dt= x(dy/dt)-y(dx/dt)/x^2
y=132ft and dx/dt=264ft/sec
How do I find x. or where do I go from here
I think I understand the problem now.
t is the independant variable, time.
x is the position of the car.
a is the angle of the camera.
You can call them whatever you like, but those are the three quantities we're measuring. We're trying to find , the angle change per second. They tell us what is when they tell us the speed of the car. We then have to find so we can plug it into the equation below.
That's why you need to find the derivative of the equation in my first reply.