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The purpose of Lab Assignment 1 was to analyze projectile motion by determining the initial velocity of a ball shot horizontally from a spring-loaded projectile launcher, identifying the angle that produces maximum range, and predicting the range at a given angle. The experiment involved measuring the range of the projectile at various angles, finding the initial velocity, and analyzing the relationship between velocity and range. The results indicated a 10% deviation from theoretical values, suggesting potential sources of error.

Projectile motion is the motion of objects launched into the air, moving under the influence of gravity.

It is characterized by two main components: the initial velocity of the projected object at a specific angle and the force of gravity acting downward. By breaking down the velocity into its horizontal and vertical components, we can analyze the motion more effectively. The vertical component can be described by the equation *y = 0.5gt^2*, where *y* is the vertical displacement and *t* is the time of flight.

The horizontal component is given by *x = v0x * t*, where *x* is the horizontal distance, *v0x* is the initial horizontal velocity, and *t* is the time of flight.

The initial velocity can be determined using the equation *v = 0.5g(x/y)^0.5*. In this experiment, we aimed to find the initial velocity, verify the angle for maximum range, and predict the range at a given angle. These objectives required firing a ball at different angles, measuring ranges, and comparing experimental and theoretical values. Additionally, we explored the relationship between velocity and range in projectile motion.

The experiment was conducted using a spring-loaded projectile launcher.

To achieve the objectives, we followed these steps:

- For determining the angle of maximum range, we fired the ball at angles ranging from 30 degrees to 50 degrees in 5-degree increments, measuring the range for each angle.
- For finding the initial velocity, we fired the ball horizontally and measured its horizontal range, which allowed us to calculate the initial horizontal velocity (
*v0x*). - We conducted trials at a fixed angle of 55 degrees, measuring the range for each trial to analyze the consistency of results.

The measurements for the angle of projection and corresponding range of motion are presented in the table below:

Angle of Projection (°) | Range of Motion (m) |
---|---|

30 | 2.72 |

35 | 2.79 |

40 | 2.84 |

45 | 2.85 |

50 | 2.77 |

The initial velocity (*v*) was determined using the equation:

*y = 0.5g(x/vx)*

Plugging in the experimental values, we found the initial velocity to be *2.5 m/s*.

For the trials conducted at a fixed angle of 55 degrees, the range data is as follows:

Trial # | Range (m) |
---|---|

1 | 2.63 |

2 | 2.63 |

3 | 2.59 |

4 | 2.60 |

5 | 2.62 |

The average range for these trials was *2.608 m*.

After analyzing the data, we found that the initial velocity (*v*) was *2.5 m/s* for all trials conducted. The measured range values for different launch angles ranged from *2.72 m* to *2.85 m*, with the maximum range achieved at an angle of 45 degrees. For trials at a fixed angle of 55 degrees, the average range was *2.608 m*.

The experiment aimed to determine the initial velocity, identify the angle for maximum range, and predict the range at a given angle in projectile motion. The results indicate that the initial velocity remains consistent at *2.5 m/s* for all trials, which suggests that the launcher's initial velocity is uniform.

Regarding the angle of maximum range, the data confirms that an angle of 45 degrees produces the greatest range, which aligns with theoretical expectations. This angle allows for the best balance between horizontal and vertical motion, maximizing the projectile's travel distance.

However, the comparison between the predicted and experimental range values revealed a 10% deviation. Several factors may contribute to this deviation, including measurement errors, air resistance, and the stability of the launcher. Air resistance, in particular, can significantly affect the range of a projectile in real-world conditions, and its impact may explain the observed deviation.

In conclusion, this experiment provided insights into projectile motion by determining the initial velocity, confirming the angle for maximum range, and predicting range values at various launch angles. While the initial velocity remained consistent at *2.5 m/s*, the experimental range values exhibited a 10% deviation from theoretical expectations. This deviation may be attributed to factors such as measurement errors and air resistance.

For future experiments on projectile motion, it is essential to consider the impact of air resistance and measurement accuracy. Using more precise measurement tools and conducting trials in a controlled environment with minimal air resistance can help reduce experimental deviations. Additionally, further investigations could explore the effects of varying initial velocities and launch heights on projectile motion to gain a deeper understanding of the underlying principles.

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