Imagine you're participating in a unique race called "The Great Physics Race". The race has three stages:

1. The Slippery Slope:
   1. The first stage is down a large, inclined plane covered in a frictionless material. You have a sled, and your goal is to reach the maximum speed possible by the end of this slope.
2. The Human Catapult:
   1. At the end of the slope, you'll land on a giant springboard that will launch you (safely, of course!) across a river. The angle and force of your launch will determine how far you fly.
3. The Balancing Act:
   1. Once you land, you'll find a teeter-totter (a seesaw). Your challenge is to balance it using different weights, representing different forces, to ensure it remains in equilibrium.

Questions:

1. For theSlippery Slope, how does the angle of the incline affect your speed when you reach the bottom? What would be the ideal angle to achieve maximum speed?
2. In theHuman Catapult stage, if you want to cross the widest part of the river, at what angle should you be launched? How would your projectile motion change if the springboard's force was increased?

For theBalancing Act, if a weight representing a force of 10N is placed 2m away from the fulcrum on one side, how would you balance the seesaw? Where and with what force should you place the weights on the other side?