apparently you didn't bother to follow the hint, so I'll give you a push...
dx/dt = -600 mi/hr
h = 2
tanθ = 2/x
sec^2θ dθ/dt = -2/x^2 dx/dt
Now plug in your numbers and find dθ/dt.
watch the units.
An airplane in Australia is flying at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line of sight increasing when the distance from the kangaroo to the plane is 3 miles? Give your answer in radians per minute.
Hint: The angle of elevation is that angle that the line of sight makes with the horizontal. Construct a triangle representing the situation. Use this to get a equation first involving x and y, then differentiate to involve dx/dt and dy/dt. Think about what it means that the plane is getting closer to the kangaroo.
1 answer
1 answer