Lab #7: Trajectories

Objective: To use our knowledge or projectile motion to calculate the "launch" velocity of a ball and use that to predict where the ball would impact a slanted board.

Procedure:
1. We first used our table, a ring stand, two "v-channel" rails, supports and tape to put together a slide for the metal ball to roll down and exit with only a horizontal velocity for the start of it's projectile path.

2. Because the launch point is above the floor, we had to make a plumb-bob with string and a mass to hang from the tip of the rail and find the location of our x-initial position. Using this we can better measure how far the ball travels for its x-componet. We also measured the height from the floor of the launch point to later use for our calculations.

3. We then had two test runs to see where the ball would hit the floor and taped a white paper to that area of the floor with a piece of carbon paper on top so that the impact would leave a mark so that we could measure how far it traveled horizontally.

4. Once everything was set up we ran 5 experimental trials and collected data on how far the ball had traveled along the horizontal.

5. Using our data, we broke down the ball's projectile motion into its x and y components. We made a chart of all the bits we knew for each component and used out kinematic equations to set up equations. Things that we had to keep in mind when doing this expariment was making sure the exit rail was level so that we would have no initial velocity for the y-component, understanding that there was no acceleration for the x-component and most importantly that the time used in both the x and y kinematic equations must be the same! We then used our y-component to solve for our time and plugged that into out x-kinematic equation to find our initial launch velocity for our ball.

6. Now we set up a slanted board to be flush with the exit rail and measure the angle between the board and the ground.

7. This time before our experimental runs we separate our information for each component and set up equations for each to predict where the ball should impact on the slanted board. These equations are more difficult to set up and solve than the previous ones because now we must include our angle and also understand the new distance traveled is along a diagonal and not only along one axis.

8. After predicting where the ball should impact we once again tape down a white paper with carbon paper onto the area where it should land and proceed with our five experimental runs.

9. Our calculations were right on the mark leavin us very close to our experimental values! However, because there is uncertainty in everything we do (for this experiment we have uncertainty in our measurements of both distance and the angle of the board) we must preform our propegated uncertainty calculations to make sure we are covered when reporting our results.

Our propegated uncertainty ended up giving us a range of 0.488 plus or minus .0315 meters for our distance which is more than enough for us to feel confident in our results when compared to our experimental values of the distance.