Vertical Jump Physics (Finding Height, Initial Velocity and Hang Time)
63.9 هزار بار بازدید -
8 سال پیش
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I was at a sports
I was at a sports bar watching basketball and got to thinking about jumping physics. I am going to go over a problem that has all the givens and solve for each variable using only one of the givens. So a person jumps up to a height .711 meters. This is the average height of a basketball players jump 28 inches for those of us who think in imperial. The person has a take off velocity of 3.73 meters per second and a total hang time of .762 seconds. Like I said previously we are going to solve the problem as if we only have height take off velocity and hang time. We will be using 2 equations to solve for all of the variables velocity equals acceleration times time plus velocity and position equals one half acceleration time time to the second power plus velocity time time. The things you need to understand to complete a problems like this is that the time to reach the peak is the same as the time to fall back down from peak. Also that the initial take off velocity is the same as the final landing velocity.
So lets first solve the problem as if we only have the height .711 meters. So to find the time we will use the position formula and act as if we are solving for how long it will take the basket ball player to fall down to the ground from the peak. This means that velocity is zero so it is left out of the equation. So the equation will be one half gravity time time to the second power equals height. After plugging in our numbers and rearranging the formula using algebra we get .381 seconds for the time to fall down or the time to reach the peak. To get total hang time we must multiply this number by 2 we get .762 seconds as our total hangtime. Now recall as I stated earlier velocity initial equals velocity final. So to solve for velocity we will be solving it as if the basket ball player is at its peak and falling down. Now to find velocity we can use the equation velocity equals gravity times time and plug in the time for falling down of .381. this equals 3.73 meters per second.
Now lets solve the problem as if we only have the take off velocity. Once again recall that velocity intial equals velocity final. So we will solve for the time it takes to hit the ground from peak. We can use the formula velocity equals gravity times time. There is no intial velocity due to the velocity being zero at the peak. After plugging in our numbers and rearranging the formula we get the time to fall to equal .381 seconds. To get the total hang time we must multiply this by two to get a hang time of .762 seconds. Lets now solve for height we will use the position formula of one half gravity times time squared plus velocity times time. Once we plug in all of our numbers we get a height of .711 meters
Finally lets solve the problems as if we are only given hang time. To solve for velocity we can plug our numbers into the velocity formula and treat it as if we are falling from the peak. So we will be solving for the velocity at landing. The formula gravity times hangtime over two will get us our velocity of 3.73 meters per second. Lets now solve for height we will use the position formula of one half gravity times time squared plus velocity times time. Once we plug in all of our numbers we get a height of .711 meters
That concludes this video thanks you for watching
Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.
So lets first solve the problem as if we only have the height .711 meters. So to find the time we will use the position formula and act as if we are solving for how long it will take the basket ball player to fall down to the ground from the peak. This means that velocity is zero so it is left out of the equation. So the equation will be one half gravity time time to the second power equals height. After plugging in our numbers and rearranging the formula using algebra we get .381 seconds for the time to fall down or the time to reach the peak. To get total hang time we must multiply this number by 2 we get .762 seconds as our total hangtime. Now recall as I stated earlier velocity initial equals velocity final. So to solve for velocity we will be solving it as if the basket ball player is at its peak and falling down. Now to find velocity we can use the equation velocity equals gravity times time and plug in the time for falling down of .381. this equals 3.73 meters per second.
Now lets solve the problem as if we only have the take off velocity. Once again recall that velocity intial equals velocity final. So we will solve for the time it takes to hit the ground from peak. We can use the formula velocity equals gravity times time. There is no intial velocity due to the velocity being zero at the peak. After plugging in our numbers and rearranging the formula we get the time to fall to equal .381 seconds. To get the total hang time we must multiply this by two to get a hang time of .762 seconds. Lets now solve for height we will use the position formula of one half gravity times time squared plus velocity times time. Once we plug in all of our numbers we get a height of .711 meters
Finally lets solve the problems as if we are only given hang time. To solve for velocity we can plug our numbers into the velocity formula and treat it as if we are falling from the peak. So we will be solving for the velocity at landing. The formula gravity times hangtime over two will get us our velocity of 3.73 meters per second. Lets now solve for height we will use the position formula of one half gravity times time squared plus velocity times time. Once we plug in all of our numbers we get a height of .711 meters
That concludes this video thanks you for watching
Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.
8 سال پیش
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