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OVERVIEW
The purpose of this experiment is to predict and verify the range of a ball launched at an angle. The initial speed of the ball is determined by shooting it horizontally and measuring the range of the ball and the height of the muzzle of the Mini Launcher.
The purpose of this experiment is to predict and verify the range of a ball launched at an angle. The initial speed of the ball is determined by shooting it horizontally and measuring the range of the ball and the height of the muzzle of the Mini Launcher.
LEARNING OBJECTIVES:
At the end of this module, the student is expected to:1. Measure height and length the ball travels and calculate the velocities of projectiles launched in different angles by group.2. Compute for the percentage differences of the velocities.
At the end of this module, the student is expected to:1. Measure height and length the ball travels and calculate the velocities of projectiles launched in different angles by group.2. Compute for the percentage differences of the velocities.
MOTION IN TWO DIMENSIONS
Motion in two dimensions is the motion that takes place in two different directions or coordinates simultaneously. Two-dimensional motion is the study of movement in two directions, including the study of motion along a curved path, such as projectile and circular motion. An example of two-dimensional motion (2D motion) is a clown shot out of a cannon or a volleyball set in a volleyball game. These examples denote two-dimensional projectile motion in which there is both a vertical and a horizontal component of the motion. The most important fact to remember is that motion along perpendicular axes are independent, hence should be analyzed separately. The key to analyzing two-dimensional projectile motion is to break it into two motions, one along the horizontal axis and the other along the vertical. In other words, treat each dimension of two-dimensional motion independently. Further, we must deal with velocity, acceleration, and displacement when describing motion.
Motion in two dimensions is the motion that takes place in two different directions or coordinates simultaneously. Two-dimensional motion is the study of movement in two directions, including the study of motion along a curved path, such as projectile and circular motion. An example of two-dimensional motion (2D motion) is a clown shot out of a cannon or a volleyball set in a volleyball game. These examples denote two-dimensional projectile motion in which there is both a vertical and a horizontal component of the motion. The most important fact to remember is that motion along perpendicular axes are independent, hence should be analyzed separately. The key to analyzing two-dimensional projectile motion is to break it into two motions, one along the horizontal axis and the other along the vertical. In other words, treat each dimension of two-dimensional motion independently. Further, we must deal with velocity, acceleration, and displacement when describing motion.
KINEMATIC EQUATIONS FOR 2D MOTION
Shown on the right is the kinematic equations used in two-dimensional motion. Note that it is only applicable for the vertical component since the variable y always appear in every formula. When dealing with the horizontal component, just change the y (vertical distance) to x which denotes the horizontal distance, the v0y (initial vertical velocity) to v0x which denotes the initial horizontal velocity, the vy (final vertical velocity) to vx which denotes the final horizontal velocity, and the ay (vertical acceleration) to ax which denotes horizontal acceleration. Note that in projectile motion, the vertical acceleration is -g or -9.8m/s2 while the horizontal acceleration is equal to zero. Furthermore, v0x is equal to v0cosθ while v0y is equal to v0sinθ. These formulas were utilized to derive the formula needed to solve the muzzle velocity as well as the expected horizontal distance when the projectile launcher is inclined at an angle. Shown below are the formulas derived and used in the computations for this laboratory experiment.
Shown on the right is the kinematic equations used in two-dimensional motion. Note that it is only applicable for the vertical component since the variable y always appear in every formula. When dealing with the horizontal component, just change the y (vertical distance) to x which denotes the horizontal distance, the v0y (initial vertical velocity) to v0x which denotes the initial horizontal velocity, the vy (final vertical velocity) to vx which denotes the final horizontal velocity, and the ay (vertical acceleration) to ax which denotes horizontal acceleration. Note that in projectile motion, the vertical acceleration is -g or -9.8m/s2 while the horizontal acceleration is equal to zero. Furthermore, v0x is equal to v0cosθ while v0y is equal to v0sinθ. These formulas were utilized to derive the formula needed to solve the muzzle velocity as well as the expected horizontal distance when the projectile launcher is inclined at an angle. Shown below are the formulas derived and used in the computations for this laboratory experiment.
Muzzle Velocity
Expected Distance
Salazar_BSCE2B_LR#4_Motion In Two Dimensions.pdfIn the first part, determining the horizontal speed of the ball, we used the projectile launcher projected at zero degree and at the first trigger locking position to gather horizontal distances represented as x in five trials. Then we computed the average of these horizontal distances and measured the height of the projectile launcher represented as y. By substituting these quantities to the formula above, I was able to determine the muzzle velocity or the initial horizontal speed of the ball. Note that g is -9.8m/s2. For the second part, projection at an angle, we followed almost the same procedure except that the projectile launcher should be projected at 20°. Likewise, we computed the average horizontal distances and measured the height. However, in this part, the goal is to compute for the expected distance when the launcher is at 20° using the muzzle velocity previously calculated as well as the height of the launcher, the angle 20°, and the g which is -9.8m/s2. I just substituted these quantities into the derived formula above. Then, I computed the percent difference between the computed expected distance and the actual measured distance using the formula shown in page 6 of the laboratory report. Furthermore, the last part aims to determine which projection angle gives the maximum range or horizontal distance. For instance, we fired the ball using the different angles stated in the study guide and measured each horizontal distance that the ball covered. Then, from the gathered data, we just picked the angle which gave the maximum range.
In the first part of the laboratory experiment titled “Determining the Initial Horizontal Speed of the Ball”, the muzzle velocity of the mini launcher is 3.404m/s (or 340.4cm/s). Note that this muzzle velocity is the initial horizontal speed of the ball which was determined by shooting the ball horizontally or at 0 degree. This initial velocity will then be used to calculate and predict where the ball will land when it is shot at some angle . For instance, it was utilized in the second part of the experiment titled “Projection at an Angle”, or specifically at 20°. Using the initial velocity 3.404m/s, the horizontal range x calculated is 178.8 cm. Compared to the measured horizontal range which is 169.66cm, only 5% is its percentage difference to the expected or calculated distance. This only means that the horizontal distance can be predicted in a projectile once the initial horizontal velocity is determined. In other words, the initial horizontal velocity is constant at different projection angles. Thus, it is used to predict where the ball will land. Furthermore, for the last part of the experiment, the maximum range 175.6cm was obtained when the ball was launched at 30 degrees angle. Though the textbooks say that the maximum range for a projectile motion is 45 degrees, it is legitimate that 30 degrees give the maximum range during our actual measurement. Perhaps the factor that affected this phenomenon is the air resistance since the ball is light and plastic.
REFLECTION
Motion in two dimensions means motion that occurs in two different coordinates at the same time. This motion contains the horizontal and vertical component at the same time. One common example is the projectile motion such as a a football kicked in a game, a bow shot, or a bullet fired from a gun. This laboratory experiment introduced to me the projectile launcher which is obviously used for studying the motion of projectile at different angle of projection. Personally, I enjoyed this experiment especially I was tasked in cocking the ball in the projectile launcher and firing it. I learned how to use the projectile launcher as well as appreciate its use. Furthermore, this experiment allowed me to review how to derive formulas from the given formulas. Series of algebraic manipulations happened before I got the correct derived formula. Nonetheless, I enjoyed this process since I am fond of solving algebra problems. Meanwhile, I had learned that the muzzle velocity or the initial horizontal velocity of the ball is constant regardless of the angle of projection. That is why, once it is determined using the zero degree angle, it can be used to solve the other unknown quantities in different angles of projection. Lastly, it is known that a projectile travels the farthest when it is launched at 45 degrees provided that there is no air resistance. However, the result of the actual experiment was somewhat questionable since the 30 degrees angle gave the maximum range. There is probably an error in the experiment, not sure on which part, that occurred but comparing this data to the other groups, we obtained the same angle for the maximum range.
Motion in two dimensions means motion that occurs in two different coordinates at the same time. This motion contains the horizontal and vertical component at the same time. One common example is the projectile motion such as a a football kicked in a game, a bow shot, or a bullet fired from a gun. This laboratory experiment introduced to me the projectile launcher which is obviously used for studying the motion of projectile at different angle of projection. Personally, I enjoyed this experiment especially I was tasked in cocking the ball in the projectile launcher and firing it. I learned how to use the projectile launcher as well as appreciate its use. Furthermore, this experiment allowed me to review how to derive formulas from the given formulas. Series of algebraic manipulations happened before I got the correct derived formula. Nonetheless, I enjoyed this process since I am fond of solving algebra problems. Meanwhile, I had learned that the muzzle velocity or the initial horizontal velocity of the ball is constant regardless of the angle of projection. That is why, once it is determined using the zero degree angle, it can be used to solve the other unknown quantities in different angles of projection. Lastly, it is known that a projectile travels the farthest when it is launched at 45 degrees provided that there is no air resistance. However, the result of the actual experiment was somewhat questionable since the 30 degrees angle gave the maximum range. There is probably an error in the experiment, not sure on which part, that occurred but comparing this data to the other groups, we obtained the same angle for the maximum range.
REFERENCES:
https://plato.stanford.edu/entries/physics-experiment/https://my.nsta.org/resource/94330#:~:text=Two%2Ddimensional%20(2D)%20motion,straight%20https://www.texasgateway.org/resource/analyzing-two-dimensional-motion#:~:text=Two%2Ddimensional%20motion%20is%20the,as%20projectile%20and%20circular%20motion.https://www.coursehero.com/study-guides/boundless-physics/motion-in-two-dimensions/https://www.rpi.edu/dept/phys/Dept2/APPhys1/projectile/proj/node5.htmlhttps://slideplayer.com/slide/4671839/15/images/1/Kinematics+%E2%80%93+Kinematic+Equations.jpghttps://t4.ftcdn.net/jpg/02/98/68/73/360_F_298687332_D0GAA6fAgr70NWtF8UKXPyLx0mTGug0x.jpghttps://i.pinimg.com/originals/ff/cf/d1/ffcfd1e82699b5b51e2f20438a9d8ccc.jpghttps://wallpaperaccess.com/full/53084.jpghttps://wallpaperboat.com/wp-content/uploads/2019/11/glow-universe-16.jpghttps://i.pinimg.com/originals/32/96/9c/32969c8d097e908ffa28514c98253454.jpghttps://wallpaperaccess.com/full/4149226.jpghttps://i.pinimg.com/originals/5c/ad/e6/5cade6da6c5e0eed3bc7f59e03c36c42.jpghttps://cutewallpaper.org/cdn-cgi/mirage/dd19f2d06ebc24f541f142b37b4289ffa7de722a7607e39984c5c6dd4ce8defd/1280/27x/1vzl6pojd/142661618.jpg
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