Superlesson
Project 5-2
Advanced Algebra
Chapter 5, Quadratic Functions and Relations
The English scientist Isaac Newton (1642-1727) discovered that objects attract one another with a gravitational force that depends on the masses of the objects and the distances between their centers. Because of gravity, a dropped object falls toward Earth's center.
Part A, Solving Quadratic Equations Graphically
1. Use the NAR Web site for the following questions.
a. Find the current National Association of Rocketry altitude record in the "F Altitude" event under Rule 19 in the Ages 14-18 division. Convert the record altitude to feet. Use 1 m = 3.28 ft.
b. The rocket was motionless as it began its free-fall descent from the record altitude. Use the equation h ( t ) = -16 t 2 + v 0t + h 0 to find how long after reaching its high point the rocket struck the ground (h (t ) = 0).
c. Sketch height h as a function of time t for the entire flight.
Part B, Solving Quadratic Equations by Factoring
2. Saturn's moon Titan is the second largest moon in the solar system.
a. Find the mass and radius of Earth and Titan.
b. In the metric system, the acceleration of gravity at a body's surface is a = 4.9 ¥ mass BODY (radius EARTH) 2 / massEARTH ¥ (radius BODY) 2. Find a for Titan and round it to the nearest whole number. Then write Titan's equation of free fall, h (t ) = at 2+ v 0 t + h 0.
c. A rock is ejected from a volcano on Titan at an initial height of 200 m and an initial velocity of 10 m/sec. Write the equation of free fall you can use to find how long it will take the rock to reach height 0. Write the coefficient of t 2 as a positive number.
d. Solve the equation by factoring.
Part C, Using the Quadratic Formula
3. Michael Collins was the Command Module Pilot on Apollo 11, the first successful manned lunar landing.
a. Read Collins's first comment under "Launch" to find his weight at takeoff.
b. Weight is a measure of Earth's gravitational pull on an object. An object that weighs w E pounds at Earth's surface will weigh w S pounds r miles above Earth's surface, wherer 2 + 7920r- - 15,681,600 /w E -wS, wS = 0
Use the quadratic formula to find how far above Earth's surface Astronaut Collins was when his weight measured 1 pound.
Part D, Classifying Solutions
Part E, Making Connections
4. Edwards Air Force Base in California is the touchdown site for the Space Shuttle.
a. Find the length of the runway at Edwards.
b. The distance, d, that the shuttle travels after touching down at Edwards is given by d = vt - v 2/2r where v is the shuttle's velocity, t is the number of seconds that elapse before the pilot applies the brakes, and r is the shuttle's deceleration rate. If the pilot's reaction time is 0.5 sec and the shuttle's deceleration rate is -12 ft/sec2, what is the maximum velocity at which the shuttle can land at one end of the runway without overshooting the other end?