# Motion in Two Dimensions

## Purpose

In this lab we did multiple trials shooting a ball and measuring the distance it went in specific times to reach our target. We were then able to conclude the path of the ball after we did our trials.

### Apparatus:

Photogate, Projectile Launcher, Accessory pad, meter stick, paper, carbon paper, safety glasses, ball, plunger

### Procedure:

• Part 1
• Put on safety glasses
• Mount the projectile launcher on the side of the table with a clamp. Using the built-in protractor, set the launcher to be horizontal
• The photogate, and time of flight accessory pad, work together to measure the time the projectile (ball) is in flight.

The photogate starts a timer as the projectile passes through and stops after the ball hits the pad. Connect the photogate, and pad to the capstone, and set up a time of flight timer. Add one extra digit of precision in your display.

•  Test the launcher
• Place paper and carbon paper on top of the pad
• Develop a plan to collect distance and time data for the flight of your trajectory on 5 tests.

Our plan consisted of us moving the pad to 5 different heights and distances, each time getting closer and higher, or farther away and lower, we only counted the trial if the ball hit the pad.

• Collect data for 5 points
• Plot x as a function of t. make a graph for both the short and medium range on the same plot. Create another plot for the y and t data
• Fit the data from your x(t) plots to fit your appropriate function
1. We used a linear function, to match the x and t values to the equation.

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2. We used a polynomial function to fit our y and t graph because it matched the equation
3. We found 5.8693 m/s^2 as the value for acceleration. Ideally the value would be equal to gravity at 9.8 m/s^2
4. We expect them to be them to be the same because the x value does not play an effect on the y value.
5. The height of our launcher is expressed as 0,0
6. Our predicted value did not fall between the measured values
7. Our data was fairly consistent, except for the range which was typically longer than expected.
8. Drag would make the range shorter, however in our trials we did not see drag play a role in the range.

We neglected to count for air resistance and drag. The air in the room was not a controlled environment and likely changed for every shot. We also did not re calibrate the launcher between launches, it is likely the launcher would move slightly, due to the force of the projectile being propelled out of it.

## Conclusion

Our results for this lab, were not expected, and this is due to many errors as discussed above. Acceleration should be close to 9.8m/s however we ours was calculated at 5.8693m/s. The difference of these values proves that we did not account for certain factors and must have made mistakes in our trials. Our percent errors were above 10%, this Could be due to inconsistencies with the launcher, or the other factors we didn’t calculate. If we had relized our mistakes earlier we likely could have reproduced this lab, as it was fairly simple.