Question

A plane flying with a constant speed of 29 km/min passes over a ground radar station at an altitude of 6 km and climbs at an angle of 25 degrees. At what rate is the distance from the plane to the radar station increasing 5 minutes later?

Answer 1

Explanation:

According to the diagram,

A = 90° + 25° = 115°

dc/dt = 29 km/min

distance after 5 min

c = 29 x 5 = 145 km

Use cosine rule

a² = b² + c² - 2bc Cos A

a² = 6² + c² -12cCos 115

a² = 36 + c² - 5 c .... (1)

When c = 145 km

a² = 36 + 145 x 145 - 5 x 145

a² = 21061 - 725

a = 142.6 km

Differentiate equation (1) with respect to a.

2a da/dt = 2c dc/dt + dc/dt

2 x 142.6 x da/dt = 2 x 145 x 29 + 29

285.2 da/dt = 8439

da/dt = 29.6 km/min