PHET Trajectories Lab:

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. Go to https://phet.colorado.edu/en/simulations/category/physics/motion and click on the simulation called "Projectile Motion"

2. Click on the "Play" button, and then choose "Lab"

The Cliff Simulation:

3. Drag the platform of the launcher up to some height - like 10 m, and rotate the barrel down to 0^o so that it shoots level (Like the cliff problems we solved)

4 Choose a launch speed by dragging the "Initial Speed" selector. Do not launch the projectile yet!

5. Set up a H|V table of suvat, and calculate where the projectile will land. You know for the horizontal side, velocities, and acceleration, and for the vertical side, initial velocity, acceleration, and displacement.

6. Drag the target to where the projectile will land, and hit the red "Fire" button to launch the projectile. Feel rewarded by the three stars that briefly appear. Hit the Eraser to remove the tracks after you have basked in the glow of your triumph.

7. Now move the target either farther or nearer, and calculate using another H|V table what the initial launch velocity must be to hit your target. (The reverse of what you just did)

8. Drag the slider for "Initial Speed" to the velocity that is closest to the one you calculated. (And be frustrated that it can only be integers) Hit the "Fire" button and again be rewarded. Possibly by fewer than three stars as your velocity might not have been as accurate.

The Arc Simulation:

9. 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.

10. Drag the barrel up to a jaunty angle, and select a velocity, but don't fire the cannon just yet

11. Use the Range equation (Show your work on your paper) to figure out where the projectile will land, place the target there, fire the cannon, and receive yet another three star award.

12. Move the target farther or nearer, and use the Range equation 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 that angle, and fire the cannon. Bask in your success!!

Arc Cliff: (EC)

13. Drag the launch platform up to some height like 6 m or so, and this time, tilt the barrel of the cannon up to some angle.

14. Using an H|V table predict where the projectile will land, place the target there, and fire the cannon. Feel very very rewarded!!!

15. 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.

16. 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.

The Old Lab:

Get the lab handout: Lab-VernierTrajectories.docx

Vernier 1

· Have each person in the group choose a different horizontal distance to aim for. Set up your H | V table, and solve for the horizontal velocity that each person needs to hit the target, and try it. Show your calculations of this.

· Once each person in the group has had a chance to hit the target by calculating, not by trial and error, as a group derive an equation for the launch velocity - v in terms of g – the acceleration of gravity, h – the height of the cliff, and x – the distance of the target from the base of the cliff. (hint v = s/t = x/t, solve for t from the vertical: h = ¹/₂gt², t will equal √something. Solve the variables without putting in any numbers)

Vernier 2 - A moving target!!

Here you will need to read the directions and figure out your launch speed. There are two ways to do this: figure out where the target will be when the ball gets there, or simply calculate the velocity needed to hit the target at its initial position, and add the target velocity to the velocity you just calculated. Figure this out as a group, and try a different speed to make sure your success wasn’t an accident. Remember – no trial and error. Whatever you do explain it on your lab.

Show your calculations.

Vernier 3

Use the range equation to hit the target. You could either pick any velocity and angle, and calculate the range, and then put the target there, or pick a certain velocity, and use the formula for the angle to calculate the launch angle (typically you will have to use the complement (90 – angle) of the angle you get from the angle equation) Alternately – you could pick a particular angle, and calculate the velocity needed to hit the target. Make sure everyone in the group gets a chance to hit the target their very own way.

Vernier 4 (10 pts extra credit!!!)

This is a moving target with an arc trajectory. To get extra credit you will need to have me set it up for you, and wait until I am there to type in your values and try to hit the target. You will have to explain how you did it. Trial and error is not acceptable. This is non-trivial. Use algebra without numbers to receive full extra credit. (That is derive a formula) (Hint – you will need to also specify either when or where you are going to hit the target)

Vernier ? (10 pts extra credit!!!)

Make your own challenge for people to solve. This will require some knowledge of interactive physics. We will make a shared folder of these. Have fun! (You can do these at any time after this chapter for extra credit)

Before you turn in your lab - make sure you have derived the equation I asked you to in Vernier1!!!

(If you don't understand, ask for help)