Question

I will medal and fan
I need help with part 2
Xavier is riding on a Ferris wheel at the local fair. His height can be modeled by the equation H(t) = 20cosine of the quantity 1 over 15 times t + 30, where H represents the height of the person above the ground in feet at t seconds.

Part 1: How far above the ground is Xavier before the ride begins?
Part 2: How long does the Ferris wheel take to make one complete revolution?
Part 3: Assuming Xavier begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Xavier's height above the ground reaches a minimum?

Answer 1

@jim_thompson5910 ?

Answer 2

So the H(t) function is this

\[\Large H(t) = 20\cos\left(\frac{1}{15}t+30\right)\]

right?

Answer 3

Yea solved it and got 50. Is that correct?

Answer 4

so the +30 is definitely inside the parenthesis and not outside?

Answer 5

\[H(t)=20 \cos \left( \frac{ π }{ 15 }t \right)+30\] that's the equation

Answer 6

oh ok

Answer 7

So yes, plugging in t = 0 gives 50 as the output

Answer 8

at t = 0 seconds, he is at a height of 50 ft

Answer 9

Okay, what exactly do I do for the second part? That part confuses me

Answer 10

The part in red represents the coefficient for the t variable
\[\Large H(t)=20 \cos \left( {\color{red}{\frac{ π }{ 15 }}}t \right)+30\]
this is the value of B. To find the period you would use the formula

T = 2pi/B

Answer 11

So it would be \[\frac{ 2π }{ \left( \frac{ π }{ 15 } \right) }\]

Answer 12

yes, simplify that fraction

Answer 13

We can take out the pi's right? so we would now have \[\frac{ 2 }{ 15 }\]

Answer 14

\[\large \frac{ 2π }{ \left( \frac{ π }{ 15 } \right) } = \frac{2\pi}{1} \times \frac{15}{\pi} = ???\]

Answer 15

Ohh \[\frac{ 30π }{ 1π }\] ?

Answer 16

and the pi's will cancel

Answer 17

so T = 30 is the period

t is in seconds, which means the period is 30 seconds

that means the ferris wheel completes a cycle every 30 seconds

Answer 18

Okay thank you :) I'll try and see if I can get part three on my own and if not I'll let you know :)

Answer 19

alright

Answer 20

Okay I'm confused as to what the question is asking exactly

Answer 21

"Part 3: Assuming Xavier begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Xavier's height above the ground reaches a minimum?"

at time t = 0, he starts at this point here

Answer 22

how long does it take to go around the full circle?

Answer 23

30 seconds

Answer 24

so how long does it take to go from the very top, to the very bottom?

Answer 25

15 seconds

Answer 26

plug in t = 15 and tell me what you get

Answer 27

I get a decimal when I plug it into my calculator
92.83185307

Answer 28

make sure you are in radian mode

Answer 29

\[H(15)=20\left( \frac{ π }{ 15 }15 \right)+30\] \[\frac{ π }{ 15 }\times \frac{ 15 }{ 1 }=\frac{ 15 }{ 15 }=1\] \[20\left( 1 \right)+30=50\] correct?

Answer 30

Wait

Answer 31

\[H(15)=20\left( \frac{ π }{ 15 }15 \right)+30 \] \[\frac{ π }{ 15 }\times \frac{ 15 }{ 1 }=\frac{ 15π }{ 15 }=1π?\]

Answer 32

so you'll have 20*cos(pi) + 30 = ???

Answer 33

I get 49.9?

Answer 34

you should find cos(pi) = -1

try again

Answer 35

10?

Answer 36

yep 10

Answer 37

Okay so the edge of the Farris wheel is 10ft from the ground when Xavier's height above the ground reaches a minimum

Answer 38

yep the lowest it goes is 10 ft off the ground