Superlesson
Project 8-3

Foundations of Algebra and Geometry

Chapter 8, Using Ratios to Compare

Functions with curved graphs are often encountered in astrophysics, the study of the behavior of rockets and heavenly bodies.

Part A, Quadratic Functions

1. Using the Internet, answer the following questions.

a. Robert H. Goddard was the founding father of American rocketry. Find the maximum speed and height of the rockets he built between 1930 and 1935 .

b. Convert the above velocity to ft/sec by multiplying 550 by 5280, the number of feet in a mile. Then divide the product by the number of seconds in an hour. The result is the maximum speed of Goddard's rockets in ft/sec. Round to the nearest 100 ft.

c. The function y = vx 16x² gives the height, y, of a rocket x seconds after launch, where v is the initial velocity. Write the formula for Goddard's rocket.

d. Graph the function by plotting points at 5 second intervals, beginning at x = 0. Continue until the rocket returns to earth.

e. What is the maximum height reached by the rocket?

f. Compare the maximum height you found with that given in the story about Goddard. Explain the discrepancy.

Part C, Making Connections

2. About 400 years ago, the German astronomer Johannes Kepler discovered a relationship between a planet's distance from the sun and the length of time the planet takes to orbit the sun. The relationship can be expressed as a square root function.

a. Find Mars' average distance from the Sun and the length of time it takes to orbit the Sun.

b. The earth's average distance from the Sun is called an astronomical unit (AU). At the above site, find the length of 1 AU. Then express Mars' distance in AUs. Round to the nearest hundredth.

c. Express Mars' orbital time in years (1 year = 365 days). Round to the nearest hundredth.

d. Cube Mars' distance (AU). Take the square root of the result. Compare with the planet's orbital time. What do you find?

e. Complete the statement of Kepler's discovery: A planet's orbital time in years equals ______________.

f. Test the relationship using figures for Saturn.