A plane flying with a constant speed of km/min passes over a ground radar station at an altitude of km and c

Question

A plane flying with a constant speed of km/min passes over a ground radar station at an altitude of km and climbs at an angle of degrees. At what rate, in km/min is the distance from the plane to the radar station increasing minutes later?

Answer 1

This is a related rates (calculus) problem.

Draw the picture.

See the right triangle.

Label the three sides:  The hypotenuse connects the station and the plane.  The horizontal side is at the plane's altitude; its length is (x km/hr)(a hrs)(cos theta).  The vertical side is directly above the station; it's length is the sum of the initial altitude (b km) plus (x km/hr)(a hrs)(sine theta).

The climb angle is theta.

The triangle is growing as the plane climbs.  Each side is lengthening.  You want to know the rate at which the hypotenuse is increasing.  (D/dt hypotenuse).

Show the three sides as a Pythagorean relation.

hypotenuse² =  horizontal side² + vertical side².

hypotenuse = √(horizontal side² + vertical side²).

D/dt hypotenuse = D/dt√(horizontal side² + vertical side²).

Use IMPLICIT differentiation.  Look at that chapter.  Use the chain rule.  Use the product rule.  Be careful with signs of trig derivatives.  Expand.  Simplify.

Answer 2

Im sorry? I think you've missed some number out...