How to Measure a Gravity Ball Drop

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Measuring a gravity ball drop will require you to plug information into a very specific equation. Measure a gravity ball drop with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Trigonometry, Graphs, & Other Math Tips
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Video Transcript

Hello, my name is Walter Unglaub, and this is how to measure a gravity ball drop. So, for this question, what we're interested in doing is calculating or driving analytically the gravitational acceleration due to a ball being dropped from some height. So, if I initially have the ball up here where this is my initial position, y sub y, and I let go of the ball and it drops, it falls a height h that is equal to y initial minus y final, which in this case is at the origin, and so my y final is simply equal to zero. Now the equation I'm going to want to use to derive the gravitational acceleration is the position equation from kinematics, which I can write for the y direction as y final is equal to y initial plus v initial, which is the initial velocity of the ball, times the total time it took for the ball to go from the initial height back down to the ground, plus one-half the acceleration times the times squared. So, in order to derive an expression for the acceleration, I need to know all the other parameters. In this case, I know my y final is equal to zero, so I can just move all the terms that are not dependent on the acceleration to the other side of the equation and set yf equal to zero. So I'm going to have one-half at-squared is equal to minus yi minus vit. My initial velocity however is zero, so since we're just dropping the ball, we can get rid of this term, because the initial velocity is just zero, and solving for the acceleration, I multiply by two on both sides to get minus 2 times yi, and then divide by the total time squared. We notice that if the initial y position is a positive number, and the total time is also a positive number, that my overall gravitational acceleration is going to be negative, and this is because we chose a reference frame to have increasing values of position going up for y and also for x. So this is the equation one would utilize to calculate the acceleration of an object using a ball that is dropped from y initial going down to y final. My name is Walter Unglaub, and this is how to measure a gravity ball drop.


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