Matt Jones

**M.Ed., George Washington University**

Dept. chair at a high school

Matt is currently the department chair at a high school in San Francisco. In his spare time, Matt enjoys spending time outdoors with his wife and two kids.

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When an object is moving through space this object is called a projectile. Examples of **projectile motion** include a pen falling off a table, a ball thrown through the air or a cork shot from a champagne bottle. The *velocity of a falling object = 9.8 m/sec^2 x t*.

Let's talk about projectile motion. So projectile motion is any motion of an object moving through air or space and when an object is moving through air and space there's 2 forces working there, there's one the initial horizontal velocity and then there is the force of gravity which is always pulling it down to center of earth. And just to review the velocity of a falling object under the force of gravity is equal to 9.8 meters per second squared times time. So that's how we can calculate the velocity at given time after an object is released and whether it's moving horizontally or dropping straight, that vertical velocity will always be the same. So let's look at a problem you might get with projectile motion where we have an object moving in a horizontal velocity and also under the influence of gravity pulling it down.

Let's say I'm on a cliff and I've got a golf ball and I'm going to hit it in a horizontal direction 30 meters per second. After I hit it, it takes 4 seconds to hit the ground below the cliff. And I want to know what was that final velocity when that ball hit the ground. Okay well that's going to be a couple of vectors, so my first vector when I hit the ball is 30 meters per second and we'll say in the x direction okay. Now once I hit it though gravity is pulling it down, so I've got this force pulling down and that force again what's that velocity is going to be, well I'm adding up velocities here so I want say it's going to be 9.8 meters per second squared times time, in this case 4 seconds. So if I say I'm going to go ahead and simplify and say 10 meters per second and I have 4 seconds I'm going to cancel my seconds and I'm going to get 40 meters per second.

Okay, so, oops I'm sorry this is seconds squared so I would cancel one of the squares and I would have 40 meters per second. So my y velocity is 4 meters be second and again adding vectors I have 30 meters per second along the horizon or the x and I have 40 meters per second along the y. I'm going to get that as my final velocity okay. Now how can I figure out what this velocity is? Well if you look at this, I've formed a right triangle okay there's my 90 degrees okay and I can use the Pythagorean Theorem to solve this question. Where I have a squared plus b squared equals c squared. So let's go ahead and plug in a squared is going to be 900, b squared is 1600 and so c squared is 900 plus 1600 or 2500 equals c squared. So c my final velocity equals 50 meters per second so that's how I can again use that triangle and the right angle with the Pythagorean Theorem to solve a projectile motion when an object is moving in a horizontal direction initially.