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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30 ° . At what rate is the distance from the plane to the radar station increasing a minute later?

To determine

To find:

The rate at which the distance from the plane to radar is increasing.

Explanation

1. Given:

The plane flying with a constant speed  300 km/h.

2. Calculation:

The figure is as shown below.

The angle A = 30 +90 = 120

Convert the speed to per minute.

dcdt= 300kmh=  5kmmin

At 1 minute, the plane travels 5 km from A to B.

c  at the end of one minute is  5 km

AC  = 1 km

Using law of cosine,

a2= 12+ c2-2(1)c cos(120)

a2= 12+ c2-21c *(-12 )

a2= 1+c2+c

After one min  c=5 km substituting this value in above expression we can obtain value of after one minute

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