ST 552

Calculus on a Computer

Assignment 4 – Rates of Change

1. The position of an object is given by . Plot this function. Use MAPLE to find and plot the velocity and acceleration. Discuss.

2. Starting from ground level, a ball is thrown up at 15 m/s. When does it hit the ground? What was its average velocity? Average speed?

3. How fast does a calculus book hit the ground if it is thrown upward at 6 m/s from the top of a 10 m building? What if it is thrown down at 6 m/s?

4. What is the volume of a sphere in terms of the radius? What is the rate of change Explain physically.

5. How fast should a ball be thrown upward from ground level to just touch a 10 foot ceiling?

6. In a 70 degree room, the temperature of my coffee is given by .

a. What temperature does my coffee start at?

b. Does this satisfy Newton’s law of cooling (the time rate of change of the temperature is proportional to the difference in the temperature and the room temperature)?

c. Find r given that the temperature is 150 degrees after 15 minutes.

d. With this r, when does the temperature get to 100 degrees?

7. Use three steps of Newton’s method to approximate the real root of

8. Use Newton’s method to find the roots of .

9. Suppose a soccer ball is made of leather 1/8 inch thick. If the outside diameter is 9 inches, and the density of leather is assumed to be .64 oz/cubic inch, how much does the ball weigh? (Assume soccer balls are spherical.) Do this two ways: using the derivative of volume to get a linear approximation, and using the difference of the volumes of two spheres. How much do the two approaches differ?