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 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)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.

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 = -16t2 +(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 = 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. Practice x = (85cos23°)t y = -16t2 +(85sin23°)t
The fence can be graphed using the parametric equations:
x = 135
y = 10

11. 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

12. Homework
worksheet