The height of a person on a ferris wheel is measured by function h(t)=38 sin 3.5 (t-4.0)+41.?
h= height of person in feet t=represents the time in minutes.
a) At what height, to the nearest tenth, are passengers loaded onto the Ferris wheel ? what characteristics of the graph are you finding?
b) How long does is take, to the nearest tenth, to make one full revolution? what characteristic are you finding on the graph.
c) What is the maximum height a passenger will reach? what characteristic are you finding on the graph
d) what is the radius of the ferris wheel?
the equation gives you the radius (38), period (2pi/3.5) and the height of the axle (41)
what is the difficulty?
a) To find the height at which passengers are loaded onto the Ferris wheel, we need to look at the initial value or the vertical shift of the function. In this case, the initial value is 41 feet. Therefore, passengers are loaded onto the Ferris wheel at a height of 41 feet (to the nearest tenth).
b) To determine the time it takes to make one full revolution, we need to find the period of the function. The period can be calculated using the formula T = 2π/b, where b is the coefficient in front of the variable t in the function. In this case, b = 3.5. Thus, the period is T = 2π/3.5. Evaluating this expression gives the time it takes to make one full revolution (to the nearest tenth).
c) To find the maximum height a passenger will reach, we need to look at the amplitude of the function. The amplitude is the coefficient in front of the sine function, which in this case is 38. Therefore, the maximum height a passenger will reach is 38 feet (to the nearest tenth).
d) The radius of the Ferris wheel can be determined by calculating half the distance between the minimum and maximum points on the graph. Since the amplitude is 38, the maximum height is 41 (initial value) + 38 = 79 feet, and the minimum height is 41 (initial value) - 38 = 3 feet. The radius of the Ferris wheel is half the difference between these values, which is (79 - 3)/2 (to the nearest tenth).