radius of 9 m
y = 9sin(x)
full rotation every 16 seconds
y = 9sin(π/8 x)
the bottom of the wheel is 1.5 m off the ground.
y = 10.5 + 9sin(π/8 x)
starts at the top of the ride
That means we want
y = 10.5 + 9cos(π/8 x)
A ferris wheel has a radius of 9 m, making a full rotation every 16 seconds. the bottom of the wheel is 1.5 m off the ground. what is the equation (sin or cos) that models the height of a chair on the ferris wheel that starts at the top of the ride. where is x in seconds?
5 answers
Remember to use the equation y=a*cos(bx+c)+d where:
|a| is the amplitude
2π/|b| is the period, or how long the Ferris wheel takes to get back to its starting point
-c/b is the phase shift/horizontal displacement
d is the vertical shift/midline
It's better to use cosine rather than sine because the cosine function always starts at the maximum, which makes sense in the context of this problem given that the chair starts at the top of the ride.
The radius is 9m, so this means that our amplitude is |a|=|9|=9
It takes the Ferris wheel 16 seconds to make one full rotation and come back to its starting point, so our period is equal to 2π/|b|=16 where b=π/8
There's no indication of any horizontal movement, so there's no phase shift
Since the bottom of the wheel is 1.5m off the ground, this means our midline is d=1.5
Plugging in all our variables, we have for our equation y=9cos(π/8*x)+1.5 where the time elapsed is x>0
|a| is the amplitude
2π/|b| is the period, or how long the Ferris wheel takes to get back to its starting point
-c/b is the phase shift/horizontal displacement
d is the vertical shift/midline
It's better to use cosine rather than sine because the cosine function always starts at the maximum, which makes sense in the context of this problem given that the chair starts at the top of the ride.
The radius is 9m, so this means that our amplitude is |a|=|9|=9
It takes the Ferris wheel 16 seconds to make one full rotation and come back to its starting point, so our period is equal to 2π/|b|=16 where b=π/8
There's no indication of any horizontal movement, so there's no phase shift
Since the bottom of the wheel is 1.5m off the ground, this means our midline is d=1.5
Plugging in all our variables, we have for our equation y=9cos(π/8*x)+1.5 where the time elapsed is x>0
Midline should be d=10.5 not d=1.5 because it's 1.5 meters off the ground. Correct equation is y=9cos(π/8*x)+10.5
ohh i get it now, tysm!
No problem! Let me know if you have any more questions!