I was driving through northern Maine with a couple of my Physics students, and we passed by the wind farm in Mars Hill.  "I wonder," one of them said, "how fast the tip of one of those turbine blades is going."

"I wonder," the other one said, "how far we'd fly if we hung on to the blade until it was at its highest point, and then let go."

"Let's figure it out!" I said.

So we did a bit of research, and a bit of estimation.  Here's what we found:

• Based on doing the 1001-1002-10003 count that you resort to when you don't have a stop watch handy, we concluded that it took about 8 seconds for the turbine to do a complete revolution.
• The height of the turbine tower is 262 feet.
• The length of the turbine blade is 115 feet.

So...how long would my students go flying if they let go at the blade's highest point?

Elmer Fudd wants to take out Bugs Bunny with a rocket launcher.  While the rabbit is running south, Elmer aims the rocket east, and times the launch so the rocket will collide with Bugs as he passes by.

However, Bugs is rather agile, and instead of being smeared by the rocket, he leaps onto it and hangs on for dear life.  Given the information provided below (invented by my Physics students, and yes, we recognize that some of these numbers are ridiculous, but hey, they're cartoon characters, right?), what will the velocity of the rocket (and Bugs) be after the collision?

Rocket Mass: 125 kg
Rocket Velocity: 300 m/s east

Bugs Bunny Mass: 15kg
Bugs Bunny Velocity: 25 m/s south

The peak of my house is 30 feet off the ground.  The roof has a 1/3 rise-over-run, and a slant length of 18 feet.  Attached to the side of my house there is a woodshed, which stands 12 feet tall at the roof peak, where it attaches to the building, and has a 20 degree slope.  The width of the shed is 8 feet.  Oh...and the house roof overhangs a horizontal distance of one foot.

One fine day I'm sitting at the peak of my roof solving physics problems, when suddenly I lose my balance and go sliding down the roof.  Reaching the end, I go airborne momentarily, until I crash into the shed roof and continue sliding downward until I go airborne a second time, and then crash into the ground.

Assuming (as we so often do in our crazy, cartoony physics world) the coefficient of friction between me and the roof is 0, and assuming that there is no air resistance, what will my speed be when I reach the ground?

Two of my students are floating in space, so far from any star that we'll assume that none of them exert any gravitational pull on the students.

Don't ask me how they're surviving up there - that's not my problem - I'm just the Physics teacher.

The two students start out one meter away from each other, and have no velocity relative to one another.

The mass of the first student is 80 kg, and the mass of the second is 65 kg.

How many days will it be before they collide?