1. Warm - up 1) Enter the data into L1 and L2 and calculate a quadratic regression equation (STAT  calc Quadreg). Remember: time – x distance – y. 2) Find the distances after t 1 = 0.9s and t 2 = 1.1s by plugging each time into your equation from #1. 3) Use the times and distances from #2 to estimate the instantaneous velocity at 1 seconds. Time(s)0.511.522.533.54 Distance (ft).7569.751212.75129.756

2. Falling Objects The following data shows the distance a rock is from the ground after being dropped from the roof of Mr. F’s trailer. The following data shows the distance a rock is from the ground after being dropped from the roof of Mr. F’s trailer. 1) Enter this data into your calculator and find a quadratic regression model (Quadreg). Time (s) 0.10.20.30.40.50.6 Distance (ft) 14.8414.3613.5612.44119.24

3. Falling Objects D = -16t 2 + 15 D = -16t 2 + 15 2) Create a scatter plot with the equation graphed over the data. How high was the roof of Mr. F’s trailer? What we are looking for is the vertex! We need to zoom out and hit [2 nd ], [TRACE], 3:maximum. What we are looking for is the vertex! We need to zoom out and hit [2 nd ], [TRACE], 3:maximum. Vertex = (0, 15) so at time 0 the rock was 15ft above the ground. This is the height of the trailer! Vertex = (0, 15) so at time 0 the rock was 15ft above the ground. This is the height of the trailer!

4. Falling Objects D = -16t 2 + 15 D = -16t 2 + 15 3) How long did it take for the rock to hit the ground? What we are looking for is the x-intercept! We need to zoom out and hit [2 nd ], [TRACE], 2:Zero. What we are looking for is the x-intercept! We need to zoom out and hit [2 nd ], [TRACE], 2:Zero. X-intercept = 0.968 so after 0.968 seconds the rock will hit the ground! X-intercept = 0.968 so after 0.968 seconds the rock will hit the ground!

5. Free Falling Object Equation The equation h = ½ gt 2 + h o The equation h = ½ gt 2 + h o models the height of an object under the influence of gravity versus time. h: height at any given time t. g: the acceleration of earth’s gravity. t: time. h o : the initial height of the falling object.

6. Falling Objects Lets compare our equation: D = -16t 2 + 15 Lets compare our equation: D = -16t 2 + 15 to the free falling equation: h = ½ gt 2 + h o What was the initial height (h o ) the rock was dropped from? What was the initial height (h o ) the rock was dropped from? h o = 15ft What does our equation predict for the value of gravity (g)? What does our equation predict for the value of gravity (g)? ½ g = -16  g = -32 The accepted value for gravity on earth is -32ft/s 2 !

7. Designing the Hero’s Fall Turn to page 491 for Problem 5. Turn to page 491 for Problem 5. For 5a assume a building height of 30 feet For 5a assume a building height of 30 feet For 5b assume the dimensions of the truck bed are 10 ft long, 4.5 ft high, and 5 feet wide; The cab has the following dimensions 5 ft wide, 5 ft long and 7 ft high For 5b assume the dimensions of the truck bed are 10 ft long, 4.5 ft high, and 5 feet wide; The cab has the following dimensions 5 ft wide, 5 ft long and 7 ft high For 5c assume the trucks velocity is 40 mph—convert this to feet per second For 5c assume the trucks velocity is 40 mph—convert this to feet per second

8. Designing the Hero’s Fall Turn to page 492 for Problem 6 Turn to page 492 for Problem 6 Assume the equation modeling the fall is Assume the equation modeling the fall is h=-15.5t 2 +30 h=-15.5t 2 +30 Where h is height above the ground and t is time in seconds Where h is height above the ground and t is time in seconds Now do problems 7 and 8 on page 492 Now do problems 7 and 8 on page 492

9. Homework Start on page 493, do problems 1, 3 and 4 Start on page 493, do problems 1, 3 and 4

10. Velocity Worksheet