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Phy 201
Your 'cq_1_08.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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A ball is tossed upward with an initial velocity of 25 meters / second. Assume that the acceleration of gravity is 10 m/s^2 downward.
• What will be the velocity of the ball after one second?
answer/question/discussion: ->->->->->->->->->->->-> :
Ds=v0*dt+.5a*dt
Ds= (25 m/s) (1s) + .5 (-10 m/s^2)(1s)
Ds= 20 m
vAve= ds/dt
vAve= 20 m/ 1s
vAve= 20 m/s
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@& This is the average velocity on the interval. You did a good job of finding this.
However this is not the velocity of the ball at the end of 1 second.*@
• What will be its velocity at the end of two seconds?
answer/question/discussion: ->->->->->->->->->->->-> :
Ds=v0*dt+.5a*dt
Ds= 25 m/s * 2s + .5(-10 m/s^2) (2s)
Ds= 40 m
vAve= 40 m/ 2s
vAve= 20 m/s
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@& The ball slows as it rises, so this is not correct. It isn't the velocity after 2 seconds, and this isn't he ball's average velocity for the two seconds.
*@
@& If you calculate the units you will find that the first term on the right-hand side has units of meters, as it should. The second term has units of m/s, and cannot be added to the first.
You almost have the right equation to find `ds, but you've left something out (you forgot the square on the second term, which should be .5 a `dt^2).
Note however that the question asks for the velocity at the end of two seconds, not the aveage velocity for the two seconds.*@
• During the first two seconds, what therefore is its average velocity?
answer/question/discussion: ->->->->->->->->->->->-> :
The average velocity is 20 m/s during the first two seconds
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• How far does it therefore rise in the first two seconds?
answer/question/discussion: ->->->->->->->->->->->-> :
It rises 40 m in the first 2 seconds
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• What will be its velocity at the end of a additional second, and at the end of one more additional second?
answer/question/discussion: ->->->->->->->->->->->-> :
The velocity will remain 20 m/s with each additional second.
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• At what instant does the ball reach its maximum height, and how high has it risen by that instant?
answer/question/discussion: ->->->->->->->->->->->-> :
The ball reaches it maximum height at 5 seconds. At that point it has traveled 100 m.
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@& The ball starts out at 25 m/s and loses 10 m/s every second. It won't rise for 5 seconds.*@
• What is its average velocity for the first four seconds, and how high is it at the end of the fourth second?
answer/question/discussion: ->->->->->->->->->->->-> :
The average velocity is 20 m/s in the first 4 sec and will travel 80 meters in the first 4 sec
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• How high will it be at the end of the sixth second?
answer/question/discussion: ->->->->->->->->->->->-> :
The ball traveled 93 m in 6 seconds
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*#&!
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&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
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