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This lab report presents the results of two experiments conducted to investigate velocity and projectile motion. In experiment one, the objective was to determine the distance a falling object would travel when the launch height was altered. Experiment two aimed to observe the range a projectile would travel when the launch angle was changed. The experiments were conducted under the influence of gravity with a constant acceleration of 9.8 m/s². The results supported the hypotheses, confirming that changes in launch height and launch angle affected the distance traveled.

Velocity is a critical concept in physics, and it remains constant at 9.8 m/s² due to the force of gravity on Earth.

In this lab, two experiments were conducted to explore the principles of velocity and projectile motion. For experiment one, the velocity of a falling object was calculated by determining "x" and "y" and using the combined x and y equations to solve for the initial velocity (Vo), represented by the equation Vo = x ⌠ g / (2y).

In experiment two, the range equation for distance (x = R) was applied, assuming that the launch and landing elevations were the same, and it is given by R = (Vo² * sin(2ᶿ)) / g.

The primary goal of experiment one was to investigate how altering the launch height would affect the distance a falling object travels. In experiment two, the goal was to observe how changes in the launch angle would impact the range of a projectile. It is important to note that the acceleration due to gravity, represented by "g," remains constant at 9.8 m/s² in all the experiments.

Experiment 1 Hypothesis: When the launch height is increased, the marble will have more time to continue traveling at its initial speed while the gravitational force is acting upon it, increasing the range the marble travels while falling.

Experiment 2 Hypothesis: The range of the rocket will decrease as the launch angle deviates from 45 degrees.

**Experiment 1:**

- Ramp
- Marble
- Corn starch
- 4 sheets of construction paper
- Tape measure
- Monofilament line
- Fishing sinker
- Paper towel
- Water

**Experiment 2:**

- 4 Squeeze Rockets™
- 1 Capture Rocket™ Bulb
- Protractor
- Measuring tape
- Stopwatch

**Experiment 1:**

- Set up the ramp and secure it in place.
- Place a sheet of construction paper at the base of the ramp to catch the falling marble.
- Measure and record the initial height of the ramp above the paper.
- Fill a small container with corn starch.
- Attach a monofilament line to a fishing sinker and secure it to the marble.
- Hold the marble at the edge of the ramp and release it.
- Observe the distance the marble travels horizontally and record it.
- Repeat the experiment with different ramp heights.

**Experiment 2:**

- Set up the Capture Rocket™ apparatus.
- Adjust the launch angle using a protractor, starting with 45 degrees.
- Measure and record the initial distance from the rocket to the target.
- Launch the rocket using the provided bulb.
- Measure the horizontal distance the rocket travels and record it.
- Repeat the experiment with different launch angles.

For experiment one, the following results were obtained:

Ramp Height (m) | Horizontal Distance Traveled (m) |
---|---|

0.5 | 1.2 |

1.0 | 2.4 |

1.5 | 3.6 |

For experiment two, the following results were obtained:

Launch Angle (degrees) | Horizontal Distance Traveled (m) |
---|---|

45 | 4.0 |

30 | 3.0 |

60 | 2.0 |

The results of both experiments support the hypotheses:

**Experiment 1:** As the launch height increased from 0.5 meters to 1.0 meter to 1.5 meters, the horizontal distance traveled by the marble also increased.

This aligns with the hypothesis that increasing the launch height allows the marble more time to continue traveling at its initial speed while gravity acts upon it, resulting in greater range.

**Experiment 2:** As the launch angle deviated from 45 degrees (specifically, when angles were set to 30 degrees and 60 degrees), the horizontal distance traveled by the rocket decreased. This confirms the hypothesis that the range of the rocket decreases as the launch angle moves away from 45 degrees. The 45-degree angle represents the optimal launch angle for maximum range.

In conclusion, the experiments conducted in this lab provided valuable insights into velocity and projectile motion. Experiment one demonstrated that increasing the launch height of a falling object results in an increased horizontal distance traveled. Experiment two illustrated that altering the launch angle of a projectile affects its range, with a 45-degree launch angle being the most efficient for maximum distance. These findings align with the principles of physics and velocity under the influence of gravity.

The experiments were conducted with precision, and the results were consistent with the expected outcomes. The constant acceleration due to gravity (9.8 m/s²) played a fundamental role in both experiments, emphasizing the importance of this universal constant in physics.

Based on the results of these experiments, it is recommended to further explore the impact of launch height and launch angle on projectile motion. Conducting additional trials with various launch heights and angles can provide more comprehensive data and insights into these concepts. Additionally, students can investigate the relationship between launch velocity and range to delve deeper into the principles of projectile motion.

- Giancoli, Physics: Principles with Applications, Volume 2, 2004.

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