SOLUTION: Please help me solve this As you ride the Ferris wheel in park,your distance from ground varies sinusoidally with time.You are the last seat filled,and the ride starts immediately

Algebra ->  Systems-of-equations -> SOLUTION: Please help me solve this As you ride the Ferris wheel in park,your distance from ground varies sinusoidally with time.You are the last seat filled,and the ride starts immediately      Log On


   

Question 546933: Please help me solve this
As you ride the Ferris wheel in park,your distance from ground varies sinusoidally with time.You are the last seat filled,and the ride starts immediately.Let it be the number of seconds that have elapsed since you got on.It take you 10 seconds to reach the top,56feet above the ground.the diameter of the wheel is 50 feet. sketch the graph nd write an equation to represent your distance from ground..
(if graph can not be sketch on email its ok..but if it can so please)
THANK YOU
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
As you ride the Ferris wheel in park,your distance from ground varies sinusoidally with time.You are the last seat filled,and the ride starts immediately.Let it be the number of seconds that have elapsed since you got on.It take you 10 seconds to reach the top,56feet above the ground.the diameter of the wheel is 50 feet. sketch the graph nd write an equation to represent your distance from ground.
-------------
h(t) = 31 - 25*sin(2pi*t/20 + pi/2) h in feet, t in seconds
= 31 - 25*sin((pi*t + 5pi)/10)
--------------
Notice that you board the ride 6 ft above the ground.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The amplitude of the sinusoid has to vary from
6 ft above ground to 56 ft above ground.
Normally a sinusoid varies from +A to -A
where A is the amplitude, which is 25
So, if I add a constant B, I get
B + 25 = 56 and
B - 25 = 6
2B = 62
B = 31
Now I get
+31+%2B+25%2Acos%28+%28t%2Api%29%2F10+-+pi%2F2%29+
At t=0
+31+%2B+25%2Asin%28+%280%2Api%29%2F10+-+pi%2F2%29+
+31+%2B+25%2Asin%28+%28-pi%2F2%29%29+
+31+-+25+=+6+
At t = 10 sec, I have
+31+%2B+25%2Asin%28+%2810%2Api%29%2F10+-+pi%2F2%29+
+31+%2B+25%2Asin%28+%28pi%2F2%29%29+
+31+%2B+25+=+56+
At t = 20
+31+%2B+25%2Asin%28+%2820%2Api%29%2F10+-+pi%2F2%29+
+31+%2B+25%2Asin%28+2%2Api+-+pi%2F2+%29+
+31+%2B+25%2Asin%28+%283%2Api%29%2F2%29+
+31+-+25+=+6+
This seems to work. The equation is
+31+%2B+25%2Asin%28+t%2Api%2F10+-+pi%2F2+%29+
The plot is