Math problem

[User2983]

The problem is: A Ferris wheel 50 ft. in diameter makes one revolution every 40 seconds. If the center of the wheel is 30 ft above ground, how long after reaching the low point is a rider 50 ft above the ground?

My teacher told me I have to find the cosine of some angle but I didn't understand what she was talking about. Any help would be appreciated.

[C1ay]

Originally Posted by User2983

The problem is: A Ferris wheel 50 ft. in diameter makes one revolution every 40 seconds. If the center of the wheel is 30 ft above ground, how long after reaching the low point is a rider 50 ft above the ground?

My teacher told me I have to find the cosine of some angle but I didn't understand what she was talking about. Any help would be appreciated.

Well, here's some food for thought. A horizontal line across the center of the wheel would be 30 feet above the ground. A rider 50 feet above the ground would have to be 20 feet above this line. The radius of the circle you have given is 25 feet. The sine of the angle will be a ratio of two of these. Write back if you need more help.

[User2983]

Originally Posted by C1ay

Well, here's some food for thought. A horizontal line across the center of the wheel would be 30 feet above the ground. A rider 50 feet above the ground would have to be 20 feet above this line. The radius of the circle you have given is 25 feet. The sine of the angle will be a ratio of two of these. Write back if you need more help.

Isn't the starting point of the bottom of the ferris wheel 5 feet off the ground? Would the time be 20 seconds because we want to find how long it takes to make 1/2 of a revolution, right?

[C1ay]

Originally Posted by User2983

Isn't the starting point of the bottom of the ferris wheel 5 feet off the ground?

Yes

Originally Posted by User2983

Would the time be 20 seconds because we want to find how long it takes to make 1/2 of a revolution, right?

No. 20 seconds is the time it takes to make half a revolution. If the wheel is 5 feet off the ground then the top of the wheel would be 55 feet above the ground. A rider will reach 50 feet before he gets to the top of the wheel.

Perhaps this diagram will help.

[Qfwfq]

Originally Posted by User2983

My teacher told me I have to find the cosine of some angle but I didn't understand what she was talking about.

Actually, you would have to find the angle having the right cosine: 20 ft divided by 30 ft = 2/3:

cosin(x) = 2/3

So x = arccos (2/3). This is the angle lacking from an exact half round, so you can work out what fraction of a whole round which is also the fraction of 40 seconds time.

[C1ay]

Couldn't you use the arcsin of 20/25? The dotted line is the sine of the angle isn't it?

[Qfwfq]

Ah, yes!

After going through it, thinking what to say, I took 30 instead of 25 for the radius.