9-4 Quadratic Equations and Projectiles

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Presentation transcript:

9-4 Quadratic Equations and Projectiles A model rocket is shot at an angle into the air from the launch pad. 1. The height of the rocket when it has traveled horizontally x feet from the launch pad is given by h = - .163x² + 11.43x. A. Graph this equation x= -b 2a y x 15 25 35 45 55 70 y 200 150 100 50 x 10 20 30 40 50 60 70

B. A 75 ft. tree, 10 ft. from the launch pad, is in the path of the rocket. Will the rocket clear the top of the tree? Sec. 9-4

2. The rockets height h at t seconds after launch is given by h = -22.2t² + 133t . a. Graph this equation. b. How high is the rocket in 2 sec.? x 1 2 3 4 5 6 y y 200 150 100 50 x 1 2 3 4 5 6 Sec. 9-4

General Formula for the Height of a Projectile over Time Let h be the height (in feet) of a projectile launched with an initial velocity v feet per second and an initial height of s feet. Then, after t seconds, h = -16t² + vt + s . Since 16ft ≈ 4.9 meters, if the units are in meters in the formula above, then h = -4.9t² + vt + s .

1. A ball is thrown from an initial height of 10 feet with an initial velocity of 64 feet per second. a. Write an equation describing the height h in feet of the ball after t seconds. b. How high will the ball be after 3 seconds? c. What is the maximum height of the ball?

2. An object is dropped from an initial height of 40meters. a. Write a formula describing the height of the object (in meters) after t seconds. b. After how many seconds does the object hit the ground? c. What is the maximum height of the object?

3. Suppose a ball is thrown upward with an initial upward velocity of 30 meters per second from an initial height of 10 meters. a Write a formula for the height in meters of the object after t seconds. b. Estimate when the ball is 40 meters high.