Answer to Question #64599 in Calculus for Leo

Question

4. An airplane flying horizontally at an altitude of y = 3 km and at a speed of
480 km/h passes directly above an observer on the ground. How fast is the
distance D from the observer to the airplane increasing 30 seconds later?

5. A kite is rising vertically at a constant speed of 2 m/s from a location at
ground level which is 8 m away from the person handling the string of the
kite
(a) Let z be the distance from the kite to the person. Find the rate of change
of z with respect to time t when z = 10.
(b) Let x be the angle the string makes with the horizontal. Find the rate
of change of x with respect to time t when the kite is y = 6 m above
ground.

6. A balloon is rising at a constant speed 4m/sec. A boy is cycling along a
straight road at a speed of 8m/sec. When he passes under the balloon, it is
36 metres above him. How fast is the distance between the boy and balloon
increasing 3 seconds later.