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**Today in Precalculus Go over homework**

Notes: Simulating Projectile Motion Homework

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**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.

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**Simulating Projectile Motion**

The path of the object is modeled by the parametric equations: x=(v0cosθ)t y= -16t2 + (v0sinθ)t +y0 Note: 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.

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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 = -16t2 +(150sin18°)t + 3 The fence can be graphed using the parametric equations: x = 400 y = 20

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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 = sec How high up the wall does the ball hit? y=-16(2.804)2 + (150sin18°)(2.804)+3 = 7.178ft

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**Example What happens if the angle is 19°?**

The ball still doesn’t clear the fence.

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**Example What happens if the angle is 20°?**

The ball still doesn’t clear the fence.

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**Example What happens if the angle is 21°?**

The ball just clears the fence.

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**Example What happens if the angle is 22°?**

The ball goes way over the fence.

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**Practice x = (85cos23°)t y = -16t2 +(85sin23°)t**

The fence can be graphed using the parametric equations: x = 135 y = 10

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t: 0,3 x: 0,140 y: 0, 30 How long does it take until the ball passes the cross bar? 135= (85cos23°)t t = sec How high is the ball when it passes the cross bar? y=-16(1.725)2 + (65sin23°)(1.725) = 9.681ft

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Homework worksheet

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6.3 Parametric Equations and Motion

6.3 Parametric Equations and Motion

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