## Escape Velocity

### Johnny WolfeSanta Rosa District Schools

#### Description

The ability to use and compute roots is often a necessary tool in physics. For example, square roots are used to compute the minimum velocity a spacecraft must have to escape the gravitational force of a planet.

#### Objectives

Associates verbal names, written word names, and standard numerals with integers, rational numbers, irrational numbers, real numbers and complex numbers.

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

#### Materials

-Overhead transparencies (if examples are to be worked on overhead) for ESCAPE VELOCITY (see attached file)
-ESCAPE VELOCITY EXAMPLES (see attached file)
-ESCAPE VELOCITY WORKSHEET (see attached file)
-ESCAPE VELOCITY CHECKLIST (see attached file)

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for ESCAPE VELOCITY EXAMPLES. (See attached file.)

2. Have marking pens (for overhead).

3. Have ESCAPE VELOCITY EXAMPLES prepared and ready to demonstrate to students. (See attached file.)

4. Have enough copies of ESCAPE VELOCITY WORKSHEET for each student. (See attached file.)

5. Have enough copies of ESCAPE VELOCITY CHECKLIST for each student. (See attached file.)

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills, such as addition, subtraction, multiplication, division, exponents, fractions, decimals, scientific notation, square roots and working with units. NOTE: This lesson does not address irrational numbers and complex numbers.

1. Discuss gravity with students. Then ask if it is possible to generate enough velocity to launch an object into space. (Get student comments.)

2. Discuss escape velocity. (See #1 on attached file: ESCAPE VELOCITY EXAMPLES.) Answer student questions and comments.

3. Discuss square roots and their place in physics. (See #2 on attached file: ESCAPE VELOCITY EXAMPLES.) Answer student questions and comments.

4. Discuss escape velocity formula. (See #2 on attached file: ESCAPE VELOCITY EXAMPLES.) Answer student questions and comments.

5. Discuss how mass and gravity affect escape velocity. (See #3 on attached file: ESCAPE VELOCITY EXAMPLES.) Answer student questions and comments.

6. Work example #4. (See attached file: ESCAPE VELOCITY EXAMPLES.) Answer student questions and comments.

7. Discuss the units to be used and what makes up a Newton. (See #5 on attached file: ESCAPE VELOCITY EXAMPLES.)

8. Show students why the units cancel out and become meters per second. (See #6 on attached file: ESCAPE VELOCITY EXAMPLES.)

9. Discuss Thought Provoker. (See #7 on attached file: ESCAPE VELOCITY EXAMPLES.) Answer student questions and comments.

10. Discuss Thought Provoker. (See #8 on attached file: ESCAPE VELOCITY EXAMPLES.) Answer student questions and comments.

11. Discuss Thought Provoker. (See #9 on attached file: ESCAPE VELOCITY EXAMPLES.) Answer student questions and comments.

12. Distribute the ESCAPE VELOCITY WORKSHEET. (See attached file.)

13. Distribute the ESCAPE VELOCITY CHECKLIST. (See attached file.)

14. The students will write their response on the worksheet.

15. Move from student to student observing the students' work and lending assistance.

#### Assessments

The student worksheet will be collected and scored according to the ESCAPE VELOCITY CHECKLIST. (See attached file.)

#### Extensions

Have students determine the mass or size of a planet if they are given the escape velocity of a planet and the radius.