The Drop

Suppose a roller coaster ride begins by climbing to a height of 50 meters, and then falling rapidly to a height of 10 meters. If you ignore the effects of friction, then as it falls its velocity will be related to its height above the ground by this equation:

50 - h = v²/19.6

(h = height in meters, v = velocity in meters per second)

Solve the above equation for velocities, given heights, or for heights, given velocities.

Subject: Mathematics
Topics: Algebra—Expressions and Equations
Grades: 6 - 12
Knowledge and Skills:
- Can evaluate expressions by substituting values for variables
- Can simplify expressions using correct order of operations
- Can do basic operations on both sides of an equation in such a way as to preserve the equality

Download Teacher Guide: The Drop (PDF)
Download Student Lesson: The Drop (PDF)

Roller CoastersRoller Coasters:

Designing thrilling, but safe, roller coasters requires a healthy respect for the laws of physics combined with a visionary's attitude that "the sky is the limit."
Running time 2:00 minutes.

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