Arc PHET
Feel free to work with a partner, but make your lab different from theirs by choosing different distances, and velocities. Do your own calculations. You will turn in your own work on a sheet of paper as evidence you did this lab.
1. Click Here to launch the simulation and then choose "Lab"
2. Drag the height of the launcher down so that it is launching from an elevation of 0 m. Note that it really launches from the hinge + sign, so don't worry that the barrel is higher than 0 m.
3. Drag the barrel up to a jaunty angle, and select a velocity, but don't fire the cannon just yet, and select some velocity besides the one it defaults to.
4. Use the Range equation (Show your work on your paper: Range = v2/g Sin(2 Theta) ) to figure out where the projectile will land, place the target there, fire the cannon, and receive yet another three star award.
5. Move the target farther or nearer, and use the Range equation (Low: Theta = Sin-1(g Range/v2)/2 , High: 90 - Theta)to solve for the proper launch angle (Using the same velocity) to hit the target where it now is. Show this on your paper. Move the barrel to both angles that work, and fire the cannon for both. If the small angle is less than 25o, you will only be able to fire at the high angle. That's OK. Bask in your success!! (Strut around the room saying things like "Oh Yeah")
6. Pick a velocity and an angle between 25o and 65o. Launch the cannon, and move the target to where it hits the ground. Don't erase the track. Then try firing the cannon at the complement of the angle you picked. Notice that it lands in the same place. (Complement is (90 - angle) - so if you shot the cannon at 30o, the complement is 60o) Do this again for another angle.
Arc Cliff: (Extra Credit and optional)
7. Drag the launch platform up to some height like 6 or 10 m or so, and this time, tilt the barrel of the cannon up to some angle. (The angle does not necessarily have to be jaunty.)
8. Using an H|V table predict where the projectile will land, place the target there, and fire the cannon. Feel very very rewarded!!! Notice that your X on the Vertical side is not zero, it's whatever the height of the cliff is, on ly negative...
9. Make Range Equation for a cliff problem where you are shooting off of a cliff that will predict where the projectile will land. Ideally it should be able to seamlessly deal with a net decrease of elevation, or a net increase of elevation. (Super Hard)
10. Make an equation for the Angle you have to choose to hit a target at a particular range, and for a cliff of a particular elevation. (Suuuuuuuper Hard)