Chapter 6.4, Problem 31E

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11th Edition

Ron Larson + 1 other

ISBN: 9781337275347

Textbook Problem

Falling Object In Exercises 31 and 32, consider an object with a mass of 4 kilograms dropped from a of

1500 meters, where the air resistance is proportional to the velocity.

Write the velocity of the object as a function of time *t* when the velocity after 3 seconds is approximately 31 meters per second. What is the limiting value of the velocity function?

To determine

**To calculate:** The velocity function and its limiting value when an object of 4 kilogram mass is dropped from the height of 1500 meters where air resistance and velocity are proportional to each other and the velocity reaches approximately 31 meters per second after 5.

Explanation

**Given:**

When an object of 4 kilogram mass is dropped from the height of 1500 meters where air resistance and velocity are proportional to each other and the velocity reaches approximately 31 meters per second after 5

**Formula Used:**

The integration of:

**Calculation:**

Since, air resistance and velocity are proportional to each other so

Consider the equation is;

Here

Substitute

Rearrange the equation as follows

Now, use the separation of variables method,

Integrate both the sides,

Where,

Put

Therefore,

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