Subject:
Mathematics

Topics: AlgebraExpressions and Equations
Common Core State Standard: A-REI.2,
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

Lesson:

1.

 h (meters) v (meters/sec) 15 26.2 40 14.0 35 17.1 5 29.7 30 19.8 50 0.0 25 22.1 20 24.2 45 9.9 10 28.0 0 31.3

2. 31.3 meters/sec

3. No. For the 50 foot roller coaster, the increase in velocity in the first half of the fall (from h = 50 feet to h = 25 feet) is 22.1 meters/sec. The increase in velocity in the second half of the fall (from 25 feet to 50 feet) is only 9.2 meters/second (31.3 – 22.1). So the velocity does not double when the length of the drop doubles.

### The Drop

Suppose a roller coaster ride begins by climbing to a height of 50 meters, stopping briefly, and then falling rapidly to ground level (a height of 0 meters).

As it falls the roller coaster will gain speed.

If you ignore the effects of friction, then height and speed are related by this equation:

50 – h = v²/19.6

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

1. Find the missing values in the table below:

 h (meters) v (meters/sec) 15 ? 40 ? ? 17.1 5 ? ? 19.8 ? 0.0 25 22.1 ? 24.2 ? 9.9 ? 28.0 0 ?

2.

a) What is the velocity halfway to the bottom of “The Drop”, where h = 25?

b) What is the velocity at the bottom of the drop, where h = 0?

3. If you made the roller coaster twice as high, do you think the velocity at the bottom be twice as great? Explain your answer