Question

An airplane is flying on a flight path, that will take it directly over a radar tracking station, the distance is decreasing at a rate of 400 miles per hour, when miles what is the speed of plane??​

Answer 1

Answer:

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Answer 2

Given:

The distance is decreasing at a rate of 400 miles per hour when s = 10 miles

To find: the speed of the plane

Step-by-step explanation:

[ Refer to the attached figure. ] The plane is at A.

Let CA = x be the horizontal distance of the plane from the station.

When s = 10 miles, from ABC triangle, using Pythagorean theorem, we get

BC² + CA² = AB²

⇒ 6² + x² = s² = 10²

⇒ x² = 10² - 6² = 100 - 36 = 64

⇒ x² = 8²

⇒ x = 8

Here we must understand that the distance is decreasing at a rate of 400 miles per hour when s = 10 miles, i.e.,

ds/dt = - 400 when s = 10

Now we have to find dx/dt when s = 10 and x = 8.

Again from ABC triangle, we obtain,

x² + 6² = s²

⇒ 2 dx/dt = 2 ds/dt, differentiating both sides with respect to time (t)

⇒ x dx/dt = s ds/dt

⇒ dx/dt = s/x * ds/dt

⇒ dx/dt = 10/8 * (- 400)

⇒ dx/dt = - 500

Since the distance x is decreasing, we have obtained dx/dt = - 500, a negative value.

Answer:

Therefore the speed of the plane is 500 miles per hour.