A plane flying with a constant speed of 19 km/min passes over a ground radar station at an altitude of 12 km and climbs at an angle of 35 degrees. At what rate is the distance from the plane to the radar station increasing 3 minutes later

18.559 km/min

Step-by-step explanation:

Horizontal and vertical velocities of the plane:

Vx = 19*cos (35) = 15.5639

Vy = 19*sin (35) = 10.898

Location of plane after 3 minutes will be:

X-component = Vx * 2 = 15.5639 * 2 = 31.1278 km

Y-component = 12 + (Vy * 2) = 12 + (10.898 * 2) = 33.796 km

Angle to the radar station (measured relative to ground) will be given as;

Angle = tan^ (-1) (Y-component/X-component) = tan^ (-1) (33.796/31.1278) = 47.35°

Thus;

Velocity component along the line between the radar and the plane:

Vt = 19 * cos (47.3534° - 35°)

Vt = 19 * cos 12.3534

Vt = 19 * 0.9768

Vt = 18.559 km/min