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Old Aug 22nd 2012, 10:22 AM   #1
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Problem about free falling bodies

1. A basketball player jumps straight upward to rebound a ball. He was in air for 0.8 seconds. What is his Initial Velocity and highest displacement?

Well since the absolute values of the acceleration is equal (-9.8 and 9.8) while jumping and falling back, I assume he spent the first half on ascent and the other half for decent.

Using the formula d=1/2at^2, I get this:

d=1/2(9.8)(0.4)^2
d=0.784 m

For Vi, Vi= Square Root of 2gd
Vi=sqrt of 2(9.8)(0.784)
Vi= 3.92 m/s

Another formula for Vi is Vi=gt
Vi=(9.8)(0.8)
Vi= 7.84

Something tells me that I messed up somewhere. I mean a basketball player that can only jump 0.78m? How do I check if my displacement and initial velocity is right? Aside from using Projectile Motion.

Also if an object is launched upward,, a= -9.8 m/s^2. It usually results to a negative displacement. How do I show a proper solution?
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Old Aug 22nd 2012, 12:05 PM   #2
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You have the correct answers for both max height = 0.784m and initial vertical velocity = 3.92 m/s. But this part is incorrect:

Another formula for Vi is Vi=gt
Vi=(9.8)(0.8)
Vi= 7.84

It seems you are trying to use the formula v2-v1 = at , but what this gives you is the change in velocity of the jumper while in the air. He starts upward at +3.92m/s, and ultimately lands going at -3.92 m/s, so his change in velocity is v2-v1 = -3.92m/s - 3.92 m/s = -7.84m/s. This approach would work if you applied the fact that v2 = -v1:

v2-v1 = -gt,
v2 - v1 = -2v1, so -2v1= -gt,
v1 = gt/2 = 9.8m/s x 0.8s x 1/2 = 3.92 m/s.

As for why a basketball player can only jump 0.784 meters - it's good that you are checking your answers for "reasonableness," but I would argue that it's not an unreasonable answer. When a 6-1/2 foot player dunks the ball he only needs to jump a bit over 1 meter off the ground. so at least the answer is in the ballpark (to use a baseball metaphor). If you had gotten an answer of 190 meters then you would have good reason to think there must be an error somewhere.

One other point - it helps to get in the habit of consistently using positive values for things going up and negative values for things going down, and hence the acceleration due to gravity is always -9.8m/s^2, it's never positive.

Last edited by ChipB; Aug 22nd 2012 at 02:38 PM.
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Old Aug 22nd 2012, 10:18 PM   #3
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Thank you for the answer(again).

Last edited by RPSGCC733; Aug 22nd 2012 at 10:22 PM.
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