__Purpose__

To understand the nature of projectile motion launched horizontally as well as launched at an angle.

__Introduction__

In horizontally launched projectiles, vertical velocity V_{y} is zero and g is 9.8 m/s^{2}. If we know the vertical height of the launching position d, we can calculate time of flight using the equation d = V_{y}t + gt^{2}/2. Time of flight t = √ (d/ 4.9)

Nozzle velocity of a horizontally launched projectile can be calculated with the given vertical displacement, using the observed horizontal range, R and time of flight, t.

V = R / t where V= Nozzle velocity of projectile, R = Horizontal range and t = Time of flight

In a projectile launched at angle θ , the vertical component and the horizontal component can be calculated as V_{y} = V Sin θ and V_{x} = V Cos θ.

The time of flight can be calculated with the measured value of vertical distance d , calculated value V_{y }and acceleration due to gravity using the equation d = V_{y}t + gt^{2}/2 .

Using this time of flight and the calculated value of horizontal velocity V_{x} , the horizontal range R can be calculated using the equation R = V_{x} x t .

Repeat the experiment with different values of angle θ. Observe the horizontal range for each angle θ. Compare the observed value and calculated value of the horizontal range.

__Equipment__

Mini Launcher, Meter scale, Carbon paper, Marker, Utility clamp

__Procedure__

Fixed the mini launcher and measured its vertical height from the ground d. Calculated time of flight using equation d = V_{y}t + gt^{2}/2

Using the mini launcher, launched the ball horizontally from a desk. Arranged a carbon paper set up on the floor , a little bit away from the launcher to record the fall of the ball. Adjusted its distance from the mini launcher so that the ball falls on the carbon paper. Marked the point of hit on the carbon paper and measured the distance of that point from the mini launcher, which is the horizontal range.

Calculated the velocity of flight or nozzle velocity using the observed range and calculated time. Repeated this launching 2 more times and found the average value of the launching velocity.

Adjusted the mini launcher so that the launching can be done at an angle. Note the launching angle θ. Calculated the vertical and horizontal components of the nozzle velocity.

Measured the vertical height of the mini launcher from the ground d. Calculated time of flight using equation d = V_{y}t + gt^{2}/2. Calculated horizontal range for each angle using the equation R = V_{x} x t .

Did the launching with a mini launcher at angle θ . Measured the horizontal range for each launching angle. Compared the observed value of horizontal range with the calculated value. Repeated these steps with different launching angles.

__Observations__

**Projectile launched horizontally **

Vertical height from the ground, **d = 0.85 m**

Time of flight t = √ (d/ 4.9)

t = √ (0.85/ 4.9)

** t = 0.42 seconds**

Trials | Horizontal range R ( m) | Velocity V= R / t ( m/sec) |

1 | 2.34 | 5.57 |

2 | 2.32 | 5.52 |

3 | 2.33 | 5.55 |

Average Velocity | 5.55 |

Now use this average value of V for the following calculations with angular launching.

**Projectile launched at angle **

Time of flight, t is calculated using the equation **d = V _{y}t + gt^{2}/2**

*Table 1.1 Calculations*

*Table 1.2 Final values*

d (m) | θ^{o} | V _{y}(m/s) | V _{x}(m/s) | Time of flight (sec) | Horizontal range calculated (m) | Horizontal range observed (m) | Average Horizontal range observed R (m) | |

0.835 | 80 | 5.47 | 0.96 | 1.25 | 1.20 | 2.24 | 2.16 | 2.20 |

0.845 | 70 | 5.22 | 1.90 | 1.21 | 2.30 | 3.27 | 3.21 | 3.24 |

0.825 | 60 | 4.81 | 2.78 | 1.13 | 3.14 | 3.92 | 3.83 | 3.87 |

0.825 | 50 | 4.25 | 3.57 | 1.03 | 3.68 | 4.10 | 4.05 | 4.07 |

0.83 | 40 | 3.57 | 4.25 | 0.91 | 3.87 | 3.95 | 3.79 | 3.87 |

__Analysis__

Time of flight is the same for the ** horizontal **component and

**component of velocity.**

__vertical__During the projectile motion, the ** horizontal **component of velocity remains the same.

- In this projectile motion lab, the vertical component of velocity changes according to the
of projection.__angle__ - Identify and describe 2 possible errors that occurred or can occur during this lab activity.

As evident by the high percentage error between the calculated and observed values for the range of motion, it is clear that there were some significant sources of error present in this lab. One significant error could have been due to the inaccuracy of the angle measurer. Before starting the experiment the plum bob was detached from the angle measurer and was possibly not attached correctly prior to the start of the experiment. This could have altered the accuracy of the projectile angle, which in turn affected the range of motion observed. It is important to note however that the error in the angle measurement was evident only during higher angles. For instance, as the angle measures went from 80 to 40, the percentage error also decreased. This implies that the angle measurement was more inaccurate while doing the experiment with higher angle values. A way to counter this would be to use an alternate method to measure the angle of the projectile or to use a properly calibrated plum bob prior to the start of the experiment.

Another source of error could be measurement error caused due to the use of a meter stick. As the range of the projectile exceeded 1 meter, we had to lift up the meter stick and place it down again in order to measure the distance. This could have caused a slight inaccuracy in the observed measurement due to basic human error. A way to counter this error would have been to use a measuring tape instead of a meter stick which would have allowed a more accurate measurement of distance.

**Suggest a method to extend or change this activity including some other variables. **

While this experiment in itself is a quite interesting activity with lots of insights on various topics, I believe that a lot more variables could be added to this experiment, making it an even better activity for students. It would be highly interesting to perform the activity with a second object that differs in mass from the first object. This would allow us to learn more about the relationship between mass, distance, time and velocity. Not only that, but another change I would love to see is to perform this activity outside in open ground as that would lift some prohibitions while doing the experiment. For example, as this experiment was done inside the school, we were limited from using angles more than 80 as the higher vertical velocity of those projectiles caused them to hit the roof of the halls making us unable to calcluate the range of the projectile. Doing the experiment outside would lift these restrictions and allow us to have more freedom with the lab experiment.

__Conclusion__

The purpose of this lab was to understand the nature of projectile motion by observing the range of motion and time of flight of the projectile at different angles. Throughout the experiment the horizontal motion and then the projectile motion at different angle values were observed. The initial velocity of the projectile was then used to calculate the horizontal and vertical components of the projectile at different angles which then further allowed us to calculate the time of flight and the range of motion of the projectile. This experiment gave an interesting insight into the nature of projectile motion, and through this lab we were able to conclude that the horizontal velocity of the projectile remains constant irrespective of the angle, whereas the vertical velocity of the projectile increases as the angle measurement goes higher. This higher vertical velocity then causes the range of the projectile to decrease. As such we were able to conclude that higher the angle, higher the maximum height of the projectile and lower the range of the projectile.