## 45 Reputation

11 years, 285 days

## vector valued function, motion shuttle...

Solve, using 4000 miles for the radius of the earth.

A space shuttle is in circular orbit 150 miles above the surface of the earth. Approximate

1. the speed
2. the time required for one revolution.

## A major-league pitcher ...

Maple 12

A major-league pitcher releases a ball at a point 6 feet above the ground and 58 feet from home plate at a speed of 100 mi/hr ,

If gravity had no effect, the ball would travel along a line and cross home plate 4 feet off the ground. Find the drop D caused by gravity.

NB: in this problem the angle alpha is the angle between the horizontal and the direction of the released ball. Since the ball is dropping, alpha will be negative.

## EUREKA ! (shouted Archimedes)...

Maple 12

Archimedes supposedlly, was asked to determine whether a crown made for the king consisted of pure gold. According to

legend, he solved this problem by weighing the crown first in air and then in water. Suppose the scale read 7.84 N when the

crown was in the air and 6.84 N when it was in water.

What should Archimedes have told the king ?

## Entropy changes in a free expansion...

Suppose an ideal gas expands to four times its initial volume. From experience for this process, the initial and final

temperature are the same.

1. Using a macroscopic approach, calculate the entropy change for the gas
2. Using statistical considerations, calculate the change in entropy for the gas and show that it agrees with the answer
you obtained in part 1.

## conditional probability DICE...

What is the probability that the total of two dice will be greater than 9, given that the first die is a 5?

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