Ferris+Wheels+Day+Off

Ferris Wheelers Day Off One of the cars on the Ferris Wheel ride at Hersheypark goes all of the way around in 35 seconds. What is the linear speed of one of the cars? In addition, graph a car's height with respect to time for 2 revolutions. Mark Burkhart Kayla Corbin Alexa Rongione

__Ride Facts__ Nearly 100 feet tall including the distance from the ground. Diameter of the wheel is 88 feet 20 cars

__Formula__: V=RW
 * V**= linear speed and is what we are trying to find.
 * R**= radius(the distance from the center)
 * W**= angular speed(unit:radians per time)

__What we are trying to find.__ V=? R=44 feet W=2(3.14)/35 The 2(3.14) is the two pi and the 35 is the seconds or the amount of time it takes the wheel to go around.

__Solving__ V=44(2x3.14/35) V=44(0.17943)
 * V=7.89 feet/second(about) is the linear speed of one of the car.**

__Connection__ To solve this problem we used the linear speed equation (v=rw). V is the linear speed and we were trying to find the linear speed of the car all the way around the wheel. R is the radius. To find the radius we had to go online and look up ride facts about the ferris wheel at Hersheypark. They gave us the diameter which was 88ft. so we had to divide it by 2 and we got the quotient of 44ft. for the radius. Then we had to find the w which is 2pi divided by the time it takes the wheel to revolve which is 35 seconds. Then we plugged the numbers into the formula so it looked like this, 44(2x3.14/35) and you get the answer of 7.89 feet/second which is the linear speed of one of the cars. For graphing this problem we used the equation f(x)=-44cos(2(3.14)/35*x)-56. The -44 because it is the radius and the reason it is negative is because it has to start at the bottom. To find the amplitude you have to put 2 pi over 35 seconds. The -56 comes from the wheel being 12ft. off of the ground and the radius is 44 so you add them together. The problem is also cosine because it has to start at the bottom to show that the height is going up.

__Graph__

*The graph starts at 12ft. because the wheel is 88 ft. tall but it is 12ft. off of the ground so the person would start at 12ft. in the air.