trig 9 sylvester and tweety
Tweety and Sylvester are going to go on two different Ferris wheels. One wheel is smaller than the other. Tweety accesses the smaller wheel by a ramp which is 1 m off the ground. The wheel reaches a maximum height of 13 m. Sylvester accesses a larger Ferris wheel by a ramp that is 3.5 m above ground and reaches a maximum height of 35 m above ground. The two wheels are separated by the the ghost ship ride. When in range Sylvester is capable of springing onto Tweety's wheel by jumping across the ghost ship. At other times on the ride he cannot. Both rides last 2 minutes.
They both got on their Ferris wheels at the lowest point and at the same time. Tweety's Ferris wheel is going around 2 revolutions/minute and Sylvester's, 3 revolutions in 2 minutes. Sketch a diagram showing the wave forms for both graphs verified with your calculator. Find the times at which Tweety is within range of Sylvester. Sylvester can catch Tweety if he is ascending (rising) and is more than 6 m off the ground but less than 20 m off the ground.
They both got on their Ferris wheels at the lowest point and at the same time. Tweety's Ferris wheel is going around 2 revolutions/minute and Sylvester's, 3 revolutions in 2 minutes. Sketch a diagram showing the wave forms for both graphs verified with your calculator. Find the times at which Tweety is within range of Sylvester. Sylvester can catch Tweety if he is ascending (rising) and is more than 6 m off the ground but less than 20 m off the ground.
amplitude
Tweety: A =(max - min)/2 = (13 - 1)/2 = 6 m.
Sylvester: A = (max - min)/2 = (35 - 3.5)/2 = 15.75 m
Sylvester: A = (max - min)/2 = (35 - 3.5)/2 = 15.75 m
frequency
The frequency B is equal to the distance of 2π divided by the time for one period.
Tweety's wheel , is: 2π/30 = π/15 so B = π/15
Sylvester : is 2π/40 = π/20 so B = π/20
Tweety's wheel , is: 2π/30 = π/15 so B = π/15
Sylvester : is 2π/40 = π/20 so B = π/20
Horizontal shift
The negative cosine wave that we have been sketching to describe the motion of the wheel is the same as a sine wave that has been translated to the right on the x axis. It has moved by 1/4 or π/2.
For Tweety, this means that distance along the x axis happens to be 1/4 x one period = 1/4 x 30 = 7.5 seconds. So the value of C = 7.5 and is written as (t - 7.5)
For Sylvester, this means that distance along the x axis happens to be 1/4 x one period = 1/4 x 40 = 10 seconds. So the value of C = 10 and is written as (t - 10)
For Tweety, this means that distance along the x axis happens to be 1/4 x one period = 1/4 x 30 = 7.5 seconds. So the value of C = 7.5 and is written as (t - 7.5)
For Sylvester, this means that distance along the x axis happens to be 1/4 x one period = 1/4 x 40 = 10 seconds. So the value of C = 10 and is written as (t - 10)
Vertical shift
Both Ferris wheels are at different heights,
Tweety's wheel = (max + min )/2 = (13 + 1)/2 = 7 m above the ground, so D = 7
Sylvester's wheel = (max + min )/2 = (35 + 3.5)/2 = 19.25 m above the ground, so D = 19.25
Tweety's wheel = (max + min )/2 = (13 + 1)/2 = 7 m above the ground, so D = 7
Sylvester's wheel = (max + min )/2 = (35 + 3.5)/2 = 19.25 m above the ground, so D = 19.25
on the calculator
The Equations
Small wheel h(t) = 6sin (π/15(t - 7.5)) + 7
Large wheel h(t) = 15.75sin (π/20(t - 10)) + 19.25
Large wheel h(t) = 15.75sin (π/20(t - 10)) + 19.25
Identifying the points of interest. Sylvester on the large wheel is only in range going up. Tweety can be going up or down but if within the range of 6 to 20 m can be caught.