An airplane is flying on a flight path that will take it directly over a radar tracking station. The airplane is flying at an altitude of 6miles and s miles from the station. If s is decreasing at a rate of 400miles/hour when s=10miles. What is the speed of the Plane

Answer 1

To solve this problem, we can use the concept of related rates. Let's let the function S represent the distance between the airplane and the radar tracking station.

We are given that ds/dt = -400 miles/hour, which means that the distance S is decreasing at a rate of 400 miles/hour. We also know that when s = 10 miles, the distance S is equal to 6 miles.

Using the Pythagorean theorem, we can relate the variables s and S as follows:

S^2 = s^2 + 6^2
S^2 = s^2 + 36

Differentiating both sides with respect to time t, we get:

2S(dS/dt) = 2s(ds/dt)

Since we are interested in finding the speed of the airplane, we can substitute the given values into the equation:

2(6)(dS/dt) = 2(10)(-400)
12(dS/dt) = -8000
dS/dt = -8000/12
dS/dt = -666.67 miles/hour

Therefore, the speed of the airplane is approximately 666.67 miles per hour.