A helicopter starting on the ground is rising directly into the air at a rate of 25 ft/s. You are running on the ground starting directly under the helicopter at a rate of 10 ft/s. Find the rate of change of the distance between the helicopter and yourself (in ft/s) after 5 s.

The rate of change of the distance between the helicopter and yourself is 25.72 ft/s.

The given parameters;

The position of the helicopter after 5 s;

a = v₁t = 25 ft/s x 5s = 625 ft

b = v₂t = 10 ft/s  x 5s = 50 ft

The displacement from the initial position;

The rate of change of the distance between the helicopter and yourself is calculated as follows;

Thus, the rate of change of the distance between the helicopter and yourself is 25.72 ft/s.

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The rate of change of the distance between the helicopter and yourself (in ft/s) after 5 s is ft/ sec

Explanation:

Given:

h(t) =  25 ft/sec

x(t) = 10 ft/ sec

h(5) = 25 ft/sec . 5 = 125 ft

x(5) = 10 ft/sec . 5 = 50 ft

Now we can calculate the distance between the person and the helicopter by using the Pythagorean theorem

Lets find the derivative of distance with respect to time

Substituting the values of h(t) and  x(t) and simplifying we get,

 =  = ft / sec

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