Draw a diagram. If x is the distance from the kangaroo, then
tanθ = 2/x
sec^2θ dθ/dt = -2/x^2 dx/dt
so, when x=3, using dx/dt = -10 mi/min
13/3 dθ/dt = -2/9 * -10 = 20/9
dθ/dt = 2/3 rad/min
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.
1 answer
1 answer