A plane flying with a constant speed of 9 km/min passes over a ground radar station at an altitude of 13 km and climbs at an angle of 25 degrees.

Question

At what rate is the distance from the plane to the radar station increasing 4 minutes later?

Hint is to use the law of cosines for a triangle.

Answer 1

Let x = distance (in km) between plane and radar station at time t and let y = distance (in km) travelled by the plane in t minutes.

By the Law of Cosines, x² = 13² + y² - 2(13)(y)cos115°. Note: 115 = 90 + 25

Given: dy/dt = 9. Find dx/dt when t = 4.

When t = 4 min, y = (9 km/min)(4 min) = 36 km.

So, when t = 4, x² = 169 + 1296 - 26(36)cos115°. So, x = 43.134.

2x(dx/dt) = 2y(dy/dt) - 26(dy/dt)cos115°

2(43.134)(dx/dt) = 72(9) - 234cos115°

dx/dt = 8.66 km/min