1. Today in Precalculus Go over homework Notes: Simulating Projectile Motion Homework

2. Simulating Projectile Motion Suppose that a baseball is thrown from a point y 0 feet above ground level with an initial speed of v 0 ft/sec at an angle θ with the horizon. The initial velocity can be represented by the vector:

3. Simulating Projectile Motion The path of the object is modeled by the parametric equations: x=(v 0 cosθ)t y= -16t 2 + (v 0 sinθ)t +y 0 Note: The x-component is simply d=rt where r is the horizontal component of v 0. The y-component is the velocity equation using the y-component of v 0.

4. Example Clark hits a baseball at 3ft above the ground with an initial speed of 150ft/sec at an angle of 18° with the horizontal. Will the ball clear a 20ft fence that is 400ft away? The path of the ball is modeled by the parametric equations: x = (150cos18°)t y = -16t 2 +(150sin18°)t + 3 The fence can be graphed using the parametric equations: x = 400 y = 20

5. Example t: 0,3 x: 0,450 y: 0, 80 Approximately how many seconds after the ball is hit does it hit the wall? 400= (150cos18°)t t = 2.804 sec How high up the wall does the ball hit? y=-16(2.804) 2 + (150sin18°)(2.804)+3 = 7.178ft

6. Example What happens if the angle is 19°? The ball still doesn’t clear the fence.

7. Example What happens if the angle is 20°? The ball still doesn’t clear the fence.

8. Example What happens if the angle is 21°? The ball just clears the fence.

9. Example What happens if the angle is 22°? The ball goes way over the fence.

10. Homework Pg 531: 44,45