10.5. Applications of Parametric Equations http://www.ck12.org
Practice
Candice gets on a Ferris wheel at its lowest point, 3 feet off the ground. The Ferris wheel spins clockwise to a
maximum height of 103 feet, making a complete cycle in 5 minutes.
- Write a set of parametric equations to model Candice’s position.
- Where will Candice be in two minutes?
- Where will Candice be in four minutes?
One minute ago Guillermo got on a Ferris wheel at its lowest point, 3 feet off the ground. The Ferris wheel spins
clockwise to a maximum height of 83 feet, making a complete cycle in 6 minutes. - Write a set of parametric equations to model Guillermo’s position.
- Where will Guillermo be in two minutes?
- Where will Guillermo be in four minutes?
Kim throws a ball from (0, 5) to the right at 50 mph at a 45◦angle. - Write a set of parametric equations to model the position of the ball.
- Where will the ball be in 2 seconds?
- How far does the ball get before it lands?
David throws a ball from (0, 7) to the right at 70 mph at a 60◦angle. There is a 6 mph wind in David’s favor. - Write a set of parametric equations to model the position of the ball.
- Where will the ball be in 2 seconds?
- How far does the ball get before it lands?
Suppose Riley stands at the point (250, 0) and launches a football at 72 mph at an angle of 60◦towards Kristy who
is at the origin. Suppose Kristy also throws a football towards Riley at 65 mph at an angle of 45◦at the exact same
moment. There is a 6 mph breeze in Kristy’s favor. - Write a set of parametric equations to model the position of Riley’s ball.
- Write a set of parametric equations to model the position of Kristy’s ball.
- Graph both functions and explain how you know that the footballs don’t collide even though the two graphs
intersect.
You learned that the polar coordinate system identifies points by their angle(θ)and distance to the origin(r). Polar