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!
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.
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
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!
Sure, I'd be happy to help! However, as a Clown Bot, I'm not capable of drawing a graph but I can answer your question with a touch of humor.
First, let's find the period of the graph. The period is the time it takes for one complete cycle. In this case, we need to consider the height of the stone above the ground as Maria continues to ride her bicycle.
Since Maria picks up a stone in her tire, it will cause the height of the stone to fluctuate as she rides. The height of the stone above the ground will depend on the diameter of the bicycle's wheels, which is given as 64 cm.
To find the period, we need to calculate how long it takes for the stone to make a complete revolution, going from the highest point to the lowest point and back to the highest point again. This time will depend on the circumference of the wheel.
The circumference of a wheel can be calculated using the formula C = πd, where C represents the circumference and d represents the diameter. In this case, the diameter is 64 cm, so the circumference would be 64π cm.
Now, let's calculate the period. As Maria is riding at a speed of 21.6 km/h, we need to convert it to cm/s. There are 1000 meters in a kilometer and 100 centimeters in a meter, so we can convert 21.6 km/h to cm/s as follows:
21.6 km/h * 1000 m/km * 100 cm/m * (1/3600) h/s = X cm/s.
After calculating the above expression, we will obtain the value of X cm/s.
Finally, we can calculate the period by dividing the circumference of the wheel by the speed of the bicycle in cm/s:
Period = (64π)/(X).
And there you have it! By following these steps, you should be able to calculate the period for Maria's bicycle. I hope this helps! If you have any more questions, feel free to ask.
To find the period of the graph, which represents the stone's height above the ground as Maria continues to ride her bicycle, we need to consider the information given.
The period of a graph representing a periodic function refers to the time it takes for the graph to complete one full cycle or oscillation. In this case, the graph represents the stone's height above the ground, and the information provided is the diameter of Maria's bicycle and her speed.
To find the period, we need to consider the circumference of the bicycle wheel and the speed at which Maria is riding. We can use the formula:
Period = Circumference / Speed
First, we have the diameter of the bicycle wheel, which is given as 64 cm. The circumference can be calculated by multiplying the diameter by π (pi):
Circumference = π * diameter
Circumference = π * 64 cm
Next, we need to convert the speed from km/h to cm/s, so that the units match with the circumference:
Speed = 21.6 km/h
Speed = (21.6 km/h) * (1000 m/1 km) * (100 cm/1 m) * (1 h/3600 s)
Speed = (21.6 * 1000 * 100) / 3600 cm/s
Now, we can substitute the values into the formula to find the period:
Period = (π * 64 cm) / [(21.6 * 1000 * 100) / 3600 cm/s]
Evaluating this expression will give us the period in seconds.