Homework help?

OK, I told my daughter I was good at math and I could help her understand her homework. Wow, not such a good idea. I feel like I came in during the middle of a movie, LOL! So, it's a high school junior level course, and it's a non-traditional math class (i.e. they don't give you any formulas, or anything.) If I could just know the formula, I could probably help her. Here goes:

(the basic idea is that a person is riding a Ferris wheel, and jumping out of it into a barrel of water.)

In Homework 22: Big Push, you found the falling time for the diver if he was released from the 9 o'clock position. In that problem, the motion of the Ferris wheel gave him an initial downward velocity as he was released, and you saw that it took him less time to fall than if he had been dropped from a stationery Ferris wheel.

Now consider what happens if he is released from the 3 o'clock position. Because the platform is moving upward at that moment, the diver will start off with an initial upward motion. As in Homework 22: Big Push, his initial speed is equal to the speed with which he was moving when he was on the platform.

Assume again that the cart (that he is diving into) is in a fixed position, directly below the diver's point of release.

1) How long will it take from the time the diver is released until he reaches the water?
2) How long would it have taken him to reach the water if he had been released from a motionless Ferris wheel (at the 3 o'clock position)?

• The Ferris wheel has a raduis of 50 feet.
• The center of the Ferris wheel is 65 feet above the ground.
• The Ferris wheel turns counterclockwise at a constant rate, making a complete turn every 40 seconds.
• The water level in the cart is 8 feet above the ground.

OK - thanks for any help. I feel stupid!

Starting with #2:

At the 3 o clock position, the diver is at the same height as the center of the ferris wheel. So he/she is 65 feet - 8 feet from the surface of the water = 57 feet.
The diver needs to fall 57 feet, and you know the acceleration due to gravity is 32 feet per second(squared).

There is an equation. You need to decide which way will be positive and which way will be negative. So let's assume down is the positive direction so that acceleration due to gravity is positive 32 feet/s^2. Your equation will be

x = vo * t + (1/2) * a * t^2
57 feet = 0 + (1/2) * (32 feet/s^2) * (t^2)
57 feet = (16 feet/s^2) * (t^2)
57/16 = t^2
square root of 57/16 = t in seconds

x is the distance the diver falls.
vo is the initial velocity
t is the time it takes to fall the distance x
a is the acceleration (in this case due to gravity)

The first part of the problem is done the same way, but first you need to convert angular velocity to linear velocity. This linear velocity will be the initial velocity in the equation above. At the 3 o clock position, the diver is moving upward on the ferris wheel, so the initial velocity will be negative.

Ok, so to find linear velocity, find the circumference of the ferris wheel.
circumference = 2 * pi * radius
circumference = 2 * pi * 50
circumference = 100 * pi feet = 314 feet

So you know that the cart goes in a circle every 40 seconds. So the cart has a speed of 314feet/40s and the diver has an initial speed of -314feet/40s.

ETA: * symbol means times and ^2 means squared.

It would be best to draw a diagram of what is going on, where the diver is, how far he falls, etc. to make sense of the maths involved.

Oooookay.... yep you have fun with that! Way to feel like a on a Monday morning.
Mind you, any other morning and I wouldn't be able to help you either!
I think the more important question to ask is, why did the man want to jump off the Ferris wheel?

Ok wow!! That made my brain hurt!! I should have just skipped reading this one cuz its math and Im horrible at math!! If you ever get history questions I can help with them...


Owwowwooww my brain! lol

Originally Posted by 3CatsN1Dog

Ok wow!! That made my brain hurt!! I should have just skipped reading this one cuz its math and Im horrible at math!! If you ever get history questions I can help with them...


Owwowwooww my brain! lol

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I failed junior year math...I don't think I could be much help.

Originally Posted by Going Nova

Starting with #2:

At the 3 o clock position, the diver is at the same height as the center of the ferris wheel. So he/she is 65 feet - 8 feet from the surface of the water = 57 feet.
The diver needs to fall 57 feet, and you know the acceleration due to gravity is 32 feet per second(squared).

There is an equation. You need to decide which way will be positive and which way will be negative. So let's assume down is the positive direction so that acceleration due to gravity is positive 32 feet/s^2. Your equation will be

x = vo * t + (1/2) * a * t^2
57 feet = 0 + (1/2) * (32 feet/s^2) * (t^2)
57 feet = (16 feet/s^2) * (t^2)
57/16 = t^2
square root of 57/16 = t in seconds

x is the distance the diver falls.
vo is the initial velocity
t is the time it takes to fall the distance x
a is the acceleration (in this case due to gravity)

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NICE! I actually pretty much understand that! I wish she was just doing Trig. Now that I can handle. I hate physics.

Oh, one question. Did you set up your original equation D=RT? Cause THAT I do understand...

Well, I was going to say Cleveland, but never mind.

Originally Posted by CarolPetunia

Well, I was going to say Cleveland, but never mind.

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Bahahahaha! I like "why does he want to jump off the Ferris wheel in the first place?" Seriously. This is supposed to be a "real life" math class! LOL.

Originally Posted by kluchetta

Bahahahaha!

I like "why does he want to jump off the Ferris wheel in the first place?" Seriously. This is supposed to be a "real life" math class! LOL.

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Not to mention... how/why is the ferriswheel over water?

My brain hurts.

Originally Posted by sillyitiliangrl

Not to mention... how/why is the ferriswheel over water?

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It's in a cart. So the diver is aiming for the water in the cart. Just wait until they start the cart rolling. Now THAT makes my brain hurt!

Originally Posted by CarolPetunia

Well, I was going to say Cleveland, but never mind.

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Way way funny!

Originally Posted by kluchetta

NICE! I actually pretty much understand that! I wish she was just doing Trig. Now that I can handle. I hate physics.

Oh, one question. Did you set up your original equation D=RT? Cause THAT I do understand...

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Gosh, you all are so skeptical. Everytime I go to the fair, I take a sheet of equations and figure out how long it will take me to fall from different parts of the ferris wheel before I even think about riding!

The first part of the equation is a simple D = RT, but the second term 0.5*a*t^2 is a more complicated D=RT because gravity changes the rate at which the diver is falling. I guess if you know that you need to account for gravity and you don't know what the equation is suppose to be, I guess you could figure out the second term by seeing that you need to multiply gravity by t^2 to get the units to cancel out properly? Maybe? But, I'm not sure how anyone would figure out to put a 1/2 in front of that second term without using calculus?

The ferris wheel problem maybe isn't very practical, but I'll bet you could argue your way out of a traffic ticket using this equation if you know what the speed limit is (vo), the rate at which your car can slow down (a), and show that you wouldn't be able to stop before reaching the intersection (x, the distance from where you are to the intersection) in the time it takes for the stoplight to go from yellow to red (t).

I am stupid, but isnt gavity a constant? It does not change? I was thinking we need the surface area of the poor person falling? Just for fun, dont listen to me. You are all cool.

Yea I am dumb. The pull of gravity is diff depending on mass. AHHHH. Please dont make me think any more...OK.

Originally Posted by binkyhoo

I am stupid, but isnt gavity a constant? It does not change? I was thinking we need the surface area of the poor person falling?

Just for fun, dont listen to me. You are all cool.

Yea I am dumb. The pull of gravity is diff depending on mass. AHHHH. Please dont make me think any more...OK.

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You're not dumb! The gravity is (more or less) constant, but it causes the diver to fall faster and faster. In real life, there's a limit to how fast the diver can fall (he can't fall faster and faster forever) because of air resistance, and you're right- it does depend on his/her surface area!

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Has your daughter truned in her homework? Just curious how she did! I really cant do math like that unless I have been in class and the teacher just taught it! High school math is hard! I took Statistics and was lucky to get a C in the class! Tell your daughter good luck!!!