g A plane flying with a constant speed of 29 km/min passes over a ground radar station at an altitude of 15 km and climbs at an angle of 45 degrees. At what rate is the distance from the plane to the radar station increasing 5 minutes later

The rate at which the distance from the plane to the radar station is increasing 5 minutes later is; 28.85 km/min

Since the train passes at an altitude of 15 km.

Let us say a = 15 km

Then it climbs at an angle of 45°

Plane is flying at a speed of 29 km/min

Thus, in t minutes, it will have flown a distance of 29t km

     Now, the distance of the plane from the radar station t minutes later is gotten by Pythagoras theorem as;

x(t) = √[(29t)² + (15²)]

x(t) = √(841t² + 225)

x'(t) = dx/dt = 841t/(√(841t² + 225))

After t = 5 minutes, we have;

x'(5) = (841 × 5)/(√((841 * 5²) + 225))

x'(t) = 4205/145.7738

x'(t) = 28.85 km/min

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At 28.93 km/min is the distance from the plane to the radar station increasing 5 minutes later

Step-by-step explanation:

Refer the attached figure

We are given A plane flying with a constant speed of 29 km/min passes over a ground radar station at an altitude of 15 km

x=15 km

We will use cosine law

----1

Differentiating

----2

Substitute values in 1

z=155.96 km

Substitute values in 2

So,

Hence At 28.93 km/min is the distance from the plane to the radar station increasing 5 minutes later

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