4 answers

Maria's bicycle has a diameter of 64 cm

Question:

maria's bicycle has a diameter of 64 cm. as she rides at the speed of 21.6 km/h, she picks up a stone in her tire. draw a graph that shows the stone's height above the ground as she continues to ride at this speed for 2 s more.
can someone please help me find the period for this graph - how long it takes to complete one cycle?
thanks!

Answers

I don't think this is a cycloid
because i'm only in grade 11 math and have never heard that term before
this is from the "periodic function and their properties" unit

so, is it possible to give me an answer related to that?
thank you.

Thank you so much!.

You are dealing with a cycloid

A good start is Wikepedia, which has a nice illustration of the movement of the stone
http://en.wikipedia.org/wiki/Cycloid

Wolfram also has a good graphic.
http://mathworld.wolfram.com/Cycloid.html

they both show the equation.
careful, you have km/h and then cm and seconds, so you will have to conversions to do.

Well, it did ask you to draw the graph, and for that you can follow the path shown in the links I gave you.

For the period we simply have to know how long it takes for the wheel to make one rotation, that is, how long it takes for the stone to go from ground-level to ground-level.

The diameter of the wheel is 64π cm
it moves at 21.6 km/h
= 2160000/3600 cm/s
= 600 cm/s

since time = distance / rate
time to go 64π
= 64π/600 seconds
= .335 seconds

So roughly every 1/3 second it would complete what looks like a halfcircle.

since 2sec / .335 = appr 5.97
for a 2 second stretch of time, I would draw 6 of those loops.

for the first loop,
at t = 0, height = 0
at t = .335(1/4) , height = 32 , 1 quarter of rotation
at t = .335/2, height = 64 , half a rotation
at t = .335(3/4) , height = 32 , three-quarters of a rotation
at t = .335 , h = 0 , full rotation
draw a smooth curve to join the points.
etc..

Similar Solved Questions

1 answer
Can you please do 6 and 7 6 The Following reaction is classified as: K2CO3(aq)+BaCl2(aq)- BaCO3...
can you please do 6 and 7 6 The Following reaction is classified as: K2CO3(aq)+BaCl2(aq)- BaCO3 (s)+ 2KC[ (aq) a) acid-base neutralization reaction b) precipitation reaction c) single replacement reaction d) oxidation-reduction reaction wolH 0T (d Which one of the following is a weak acid in aque...
1 answer
Find the current through resistor R_1 and the voltage across resistor R_4.
Find the current through resistor R_1 and the voltage across resistor R_4....
1 answer
How many moles of HIO2 and its conjugate base (IO2−) are needed to create 0.45 L...
How many moles of HIO2 and its conjugate base (IO2−) are needed to create 0.45 L of a 1.00 M HIO2 buffer solution with a pH of 4.69? (The Ka of HIO2 is 3.2 ✕ 10−5.) HIO2? IO2-?...
1 answer
An article in Environment International (Vol. 18, No. 4, 1992) describes an experiment in which the...
An article in Environment International (Vol. 18, No. 4, 1992) describes an experiment in which the amount of radon released in showers was investigated. Radon-enriched water was used in the experiment, and six different orifice diameters were tested in shower heads. The data from the experiment are...
1 answer
I started this curcuit and seem to have gotten stuck how do I solve it. Problems:...
I started this curcuit and seem to have gotten stuck how do I solve it. Problems: Find the is, is, is, I, V, V2 and vg in the circuit. V=IR Vi-V2=25 Vi = 32 + V₂ o V₂ V₂ = 4i ③ AN Tv, 30 V2 D WA 10 A (1) cit la riu i=0...
1 answer
If you have a correlation coefficient of r=-.82 what type of correlation does your data have?...
if you have a correlation coefficient of r=-.82 what type of correlation does your data have? QUESTION 1 If you have a Correlation Coefficient of r = -.82. What type of correlation does your data have? Positive Linear Correlation O Negative Linear Correlation Nonlinear Correlation...
1 answer
A Randomized, Clinical Trial of Education or Motivational-Interviewing–Based Coaching Compared to Usual Care to Improve Cancer...
A Randomized, Clinical Trial of Education or Motivational-Interviewing–Based Coaching Compared to Usual Care to Improve Cancer Pain Management Mary Laudon Thomas, RN, MS, AOCN®, Janette E. Elliott, RN-BC, MS, AOCN®, Stephen M. Rao, Ph.D., Kathleen F. Fahey, RN, MS, CNS, Steven M. Paul,...
1 answer
Preparing a Classified Balance Sheet The following financial data for the Revel Corporation was collected as...
Preparing a Classified Balance Sheet The following financial data for the Revel Corporation was collected as of December 31. All accounts have normal balances. Furniture & Equipment $107,000 Accumulated Depreciation $48,800 Cash 61,000 Accounts Receivable 95,200 Common Stock 190,000 Accounts Pay...
1 answer
The change in enthalpy is the change in heat energy of a reaction and is calculated...
The change in enthalpy is the change in heat energy of a reaction and is calculated by (Hint: Hess' Law): a)Sum of product enthalpies minus the sum of reactant enthalpies b)Sum of product enthalpies times the sum of reactant enthalpies c)Sum of reactant enthalpies minus the sum of product enthal...
1 answer
1. The basis vectors for rigid body A and B initially coincide. A is held fixed...
1. The basis vectors for rigid body A and B initially coincide. A is held fixed while B is rotated by angle q: about the an, bz, direction. a) Draw the basis vectors for A and B in the final configuration. b) Determine the table of direction cosines for ARB....
1 answer
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in ...
1 answer
3. Draw the Lewis structure for the sulfate ion (1pt] a. What is the molecular geometry...
3. Draw the Lewis structure for the sulfate ion (1pt] a. What is the molecular geometry of this molecule? (0.5pt] b. What is the chemical formula for ammonium sulfate? [1pt] C. What is the molar mass of ammonium sulfate? (1pt] 4. Draw one valid Lewis structure for dinitrogen monoxide (HINT: N is the...
1 answer
SkyChefs, Inc., prepares In-flight meals for a number of major airlines. One of the company's products...
SkyChefs, Inc., prepares In-flight meals for a number of major airlines. One of the company's products is grilled salmon in dill sauce with baby new potatoes and spring vegetables. During the most recent week, the company prepared 3,500 of these meals using 1710 direct labor-hours. The company p...
1 answer
How do you write and simplify #1.30 times 10^4 div 6.5 times 10^-5# in scientific notation?
How do you write and simplify #1.30 times 10^4 div 6.5 times 10^-5# in scientific notation?...
1 answer
How do you divide #(-x^3-x^2+9x-3)/(x-3) #?
How do you divide #(-x^3-x^2+9x-3)/(x-3) #?...
1 answer
Hey guys! Looking for some help with statistics homework. These online classes have made it a...
Hey guys! Looking for some help with statistics homework. These online classes have made it a little hard to understand some of the specifc stuff like finding Z-score. 1) The average yearly Medicare Insurance benefit per person was $4064 in a recent year. The benefits are normally distributed with a...