trigonometry 8 sylvester and tweety
A bird and a cat are on two different Ferris wheels that are going in the same direction (anticlockwise). Based on the diagrams above, write equations for both Ferris wheels.
They both got on their Ferris wheels at the lowest point. Tweety's Ferris wheel is going around 2 revolutions/minute and Sylvester, 1 revolution/minute. Sketch a diagram showing the wave forms for both graphs on the same set of axis. The equations for both Ferris wheels have the same amplitude and vertical shift. Find the times at which point the bird and cat are at the same height such that the cat is directly opposite the bird so he can grab it.Good news, the bird flies away before he can be caught.
They both got on their Ferris wheels at the lowest point. Tweety's Ferris wheel is going around 2 revolutions/minute and Sylvester, 1 revolution/minute. Sketch a diagram showing the wave forms for both graphs on the same set of axis. The equations for both Ferris wheels have the same amplitude and vertical shift. Find the times at which point the bird and cat are at the same height such that the cat is directly opposite the bird so he can grab it.Good news, the bird flies away before he can be caught.
amplitude
A =(max - min)/2 = (9-1)/2 = 4 m.
So this value is the same for both wheels
So this value is the same for both wheels
frequency
The frequency B is equal to the distance of 2π divided by the time for one period. Tweety's wheel , is:
and Sylvester's wheel is
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 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 60 = 15 seconds. So the value of C = 15 and is written as (t - 15)
For Sylvester, this means that distance along the x axis happens to be 1/4 x 60 = 15 seconds. So the value of C = 15 and is written as (t - 15)
vertical shift
Both Ferris wheels are centered at 5 m above the ground, so D = 5
Writing the equations
tweety
sylvester
from the calculator
Adjust the view window settings for x, ( 60 seconds) and y ( 0 to 10 m or similar so you can see the wave form). Enter the equations into the calculator as we have learned taking note of where the brackets go. You can enter the equations in first if you like and adjust the window settings after.
Use the G-Solve (GSLV) function and select intersect (ISCT) from the sub-menu. Which point on the graph represents the point where both characters meet, the first intersection or last? The first intersection point is where Tweety is descending on the left hand side of his Ferris wheel. Sylvester is still ascending on the right hand side of his Ferris wheel so there is no contact. At 40 seconds and a height of 7 m Sylvester is able to catch Tweety.