1. There is a unicycle rolling down a flat street. The diameter of the wheel is 2 feet, and the length of the crank shaft is 8 inches. The unicycle is traveling at 10 feet/second. Determine the set of parametric equations that will determine the position of the unicyclist's foot at any given t in seconds, assuming that it starts at the 3 o'clock position, and the unicyclist is moving to the left. 2. There is a double Ferris Wheel. The large wheel is has a radius of 30 meters, and the two smaller outside wheels have radii of 10 meters each. If the large wheel rotates 0.5 revolutions per minute clockwise, and the smaller wheels rotate at 2 revolutions per minute counter clockwise, determine the location of a rider at any time t in minutes if the rider starts such that on the big wheel she is at 6 o'clock, and on the small wheel she is at 12 o'clock. 3. A lifeguard is walking from right to left along a beach at 4 m/s, while swinging their whistle around their finger in a counter clockwise rotation. The lifeguard's hand is staying at a relatively constant 1 meter above the ground. The string length is 30 cm, and it is rotating 3 times per second counter clockwise. What is the set of parametric equations that will determine the location of the whistle at any moment in time, assuming that the whistle starts at the 3 o'clock position? 4. A skier is attempting to learn how to ski on moguls. He knows that he needs to flex and extend his knees in a rhythmical way. So he does, and at his shortest, his head is 1 meter off of the ground, and at his tallest his head is 1.8 meters off of the ground. He is bouncing like this at a rate of 4 bounces per 10 seconds, and is shortest at t=0. Meanwhile his skis are on the mogul field, and following the set of parametric equations: The Unicycle: -12 -10 -8 -6 -2 0 The Double Ferris Wheel: -60 80 -40 -20 20 60 40 Rider 20 0 20 20 10 40 50 60 -2 1. There is a unicycle rolling down a flat street. The diameter of the wheel is 2 feet, and the length of the crank shaft is 8 inches. The unicycle is traveling at 10 feet/second. Determine the set of parametric equations that will determine the position of the unicyclist's foot at any given t in seconds, assuming that it starts at the 3 o'clock position, and the unicyclist is moving to the left. 2. There is a double Ferris Wheel. The large wheel is has a radius of 30 meters, and the two smaller outside wheels have radii of 10 meters each. If the large wheel rotates 0.5 revolutions per minute clockwise, and the smaller wheels rotate at 2 revolutions per minute counter clockwise, determine the location of a rider at any time t in minutes if the rider starts such that on the big wheel she is at 6 o'clock, and on the small wheel she is at 12 o'clock. 3. A lifeguard is walking from right to left along a beach at 4 m/s, while swinging their whistle around their finger in a counter clockwise rotation. The lifeguard's hand is staying at a relatively constant 1 meter above the ground. The string length is 30 cm, and it is rotating 3 times per second counter clockwise. What is the set of parametric equations that will determine the location of the whistle at any moment in time, assuming that the whistle starts at the 3 o'clock position? 4. A skier is attempting to learn how to ski on moguls. He knows that he needs to flex and extend his knees in a rhythmical way. So he does, and at his shortest, his head is 1 meter off of the ground, and at his tallest his head is 1.8 meters off of the ground. He is bouncing like this at a rate of 4 bounces per 10 seconds, and is shortest at t=0. Meanwhile his skis are on the mogul field, and following the set of parametric equations: The Unicycle: -12 -10 -8 -6 -2 0 The Double Ferris Wheel: -60 80 -40 -20 20 60 40 Rider 20 0 20 20 10 40 50 60 -2