Presentation on theme: "Today in Precalculus Go over homework"— Presentation transcript:
1 Today in Precalculus Go over homework Notes: Simulating Projectile MotionHomework
2 Simulating Projectile Motion Suppose that a baseball is thrown from a point y0 feet above ground level with an initial speed of v0 ft/sec at an angle θ with the horizon.
3 Simulating Projectile Motion The path of the object is modeled by the parametric equations:x=(v0cosθ)ty= -16t2 + (v0sinθ)t +y0Note: The x-component is simply d=rt where r is the horizontal component of v0.The y-component is the velocity equation using the y-component of v0.
4 ExampleClark 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°)ty = -16t2 +(150sin18°)t + 3The fence can be graphed using the parametric equations:x = 400y = 20
5 Examplet: 0,3x: 0,450y: 0, 80Approximately how many seconds after the ball is hit does it hit the wall?400= (150cos18°)tt = secHow 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 Practice x = (85cos23°)t y = -16t2 +(85sin23°)t The fence can be graphed using the parametric equations:x = 135y = 10
11 t: 0,3x: 0,140y: 0, 30How long does it take until the ball passes the cross bar?135= (85cos23°)tt = secHow high is the ball when it passes the cross bar?y=-16(1.725)2 + (65sin23°)(1.725)= 9.681ft