Projectile Motion Created by: Derek Zokoe ED 205 06 Click picture to enter
Index 1. About me 2. Concept Map 3. What is Projectile Motion? 4. Why is PM important? 5. Projectile motion Problem 6. Resources
About the Author My name is Derek Zokoe. I was born in Jenison Michigan. I am currently attending Grand Valley State University. I plan to graduate with a Major in physics and a Minor in Mathematics. I will also have a teaching degree. Feel free to email me. [email_address] Exit
Concept Map Exit
Exit What is Projectile Motion? In a normal sense projectile motion is just what the name says; the motion of a projectile. In a physics sense projectile motion is the study of how an object moves. You can study how water moves in the ocean, how an airplane flies in the sky, or even how a bullet flies out of the gun.
Exit Why is Projectile Motion Important? You may ask why is projectile motion important. There are many practical uses of projectile motion. Most of the real life examples are very complex. You can shoot a rocket to the moon, or study the path of a quarterbacks football throw. Not everyone needs to be an expert at projectile motion, but it is good for everyone to have a basic knowledge of how a motion will fly. Everyone knows that if an object is throw up into the air that it will come back down eventually. Well how long will it take? This is something that we can figure out quite easily using projectile motion.
Exit Projectile Motion Problem Suppose a student wants to figure out how far away an ball would land if launched off the table at an angle of 30 degrees from the horizon. The table is exactly 1 meter off the ground. The student first decides to shoot the ball straight up and tests to find how high the ball goes and how long it takes the ball to get there. He calculates that the ball travels at 10 m/s right when the ball is launched from the gun. Watch the video and then Calculate the following (use 10 m/ss for gravity) The x and y components of the initial velocity The velocity of the ball in the y direction when it is .75 above the initial height How high above the ground the ball is when it reaches its maximum How high the ball will be if traveling at 6 m/s down How fast the ball is moving just before hitting the ground Shortcut using conservation of energy
Here is a link to a video that was made. It resembles our situation very very closely. In the video the ball is launched at different angles. You do only need to calculate each value for when the ball is being launched at 30 degrees. http://paer.rutgers.edu/PT3/movies/Projectile1.mov Exit Problem
Exit Problem Initial If we use our knowledge of trigonometry we know that cos(30) is equal to the Adjacent (V x ) divided by the hypotenuse (V) and also that sin(30) is equal to the opposite (V y ) divided by the hypotenuse (V). If we use this knowledge we can derive the following equations. To calculate the initial velocity in the x direction and in the y direction.
Exit Problem On its way up We were asked to calculate the vertical velocity of ball when the ball is .75 meters above the starting point. Remember that the ball is initially being launched from 1 meter. Here is the work that will be done in solving this problem.
Exit Problem At the Top We are now supposed to find the maximum height that the ball will reach. To do so we will need to remember that the ball will have no vertical velocity when it is at its maximum point. Here is the work for this problem.
Exit Problem Coming down We are now going to be finding the height of the ball when it is traveling at a vertical speed if 6 meters per second down. Here is the work. NOTE: The initial velocity of the ball is 5 meters per second. What does this mean for the vertical position of the ball relative to the starting height?
Exit Problem At the Bottom We will finally calculate the velocity of the ball when it reaches the bottom. Remember we want the total velocity not just the vertical velocity. We will have to add the vertical velocity vector with the horizontal velocity vector. Here is the work for this problem. Now that we have the new vertical velocity we can calculate the final velocity
Back Proceed Exit Warning: The following pages will ruin your experiences of Projectile Motion
Exit Conservation of Energy Conservation of Energy can be used in every one of these problems, all of which become very easy. Since we know that the only force acting upon the ball after it is launched is gravity we know that energy will be conserved. We need to be very careful when we are calculating the height of the ball because we need to remember that potential energy is calculated from the wherever we decide our origin is. I suggest setting your origin to be the ground. Since there is not any air friction the horizontal speed will not be changing so when calculating the energy we can ignore that. Also remember when we find the final velocity of the ball just before it reaches the ground that we have calculated the velocity in the vertical direction. What is the velocity of the ball in the horizontal direction? The next page will be all of the work using conservation of energy.
Resources The opening picture: The Video I found using Yahoo video search Airplane All information and equations I learned in my Physics Class at GVSU Exit http://library.thinkquest.org/TQ0312826/index.php?chapter=3&page=2 http://paer.rutgers.edu/PT3/movies/Projectile1.mov http://www.flickr.com/photos/caribb/80279502/