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Chapter 10: Q 6. (page 643)
__________ is the collection of all points in the plane such that the distance from each point to a fixed point equals its distance to a fixed line.
Parabola is the collection of all points in the plane such that the distance from each point to a fixed point equals its distance to a fixed line.
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Projectile MotionIchiro throws a baseball with an initial speed of 145 feet per second at an angle of 20掳 to the horizontal. The ball leaves Ichiro鈥檚 hand at a height of 5 feet.
(a) Find parametric equations that model the position of the ball as a function of time.
(b) How long is the ball in the air?
(c) Determine the horizontal distance that the ball travels.
(d) When is the ball at its maximum height? Determine the maximum height of the ball.
(e) Using a graphing utility, simultaneously graph the equations found in part (a).
Find an equation for each ellipse. Graph the equation by hand.
Vertices at and : focus at.
Projectile Motion Suppose that Adam hits a golf ball off a cliff 300 meters high with an initial speed of 40 meters per second at an angle of 45掳 to the horizontal.
(a) Find parametric equations that model the position of the ball as a function of time.
(b) How long is the ball in the air?
(c) Determine the horizontal distance that the ball travels.
(d) When is the ball at its maximum height? Determine the maximum height of the ball.
(e) Using a graphing utility, simultaneously graph the equations found in part (a).
Uniform Motion A Cessna (heading south at 120 mph) and a Boeing 747 (heading west at 600 mph) are flying toward the same point at the same altitude. The Cessna is 100 miles from the point where the flight patterns intersect, and the 747 is 550 miles from this intersection point. See the figure.
(a) Find parametric equations that model the motion of the Cessna and the 747.
(b) Find a formula for the distance between the planes as a function of time.
(c) Graph the function in part (b) using a graphing utility.
(d) What is the minimum distance between the planes? When are the planes closest?
(e) Simulate the motion of the planes by simultaneously graphing the equations found in part (a).
Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.
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