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phys 201
Your 'cq_1_08.2' 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 at 15 meters / second from a height of 12 meters above the ground. Assume a uniform downward acceleration of 10 m/s^2 (an approximation within 2% of the 9.8 m/s^2 acceleration of gravity).
• How high does it rise and how long does it take to get to its highest point?
answer/question/discussion: ->->->->->->->->->->->-> :
v0 = 15 m/s
initial height = 12 m
a = -10 m/s/s
a = (vf - v0) / dt
-10 m/s = (0 m/s - 15 m/s) / dt
Dt = 1.5 s to reach highest point
ds = (v0 + vf) / 2 * dt
12m + ds = (15 m/s + 0 m/s) / 2 * 1.5
ds = 11.25m + 12 m = 23.25 m at highest point
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• How fast is it then going when it hits the ground, and how long after the initial toss does it first strike the ground?
answer/question/discussion: ->->->->->->->->->->->-> :
v0 = 0 m/s
a = 10 m/s/s
ds = 23.25 m
ds = v0 * dt +.5(a) * dt2
23.25 = 15 m/s *dt +.5(10m/s/s) *dt2
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The initial velocity, which is upward, is in the direction opposite the acceleration and the displacement, both of which are downward.
So the signs of v0, a and `ds will not all be positive.
If you are trying to find the time required to reach the ground from the highest point, which is not necessary but could be used, the initial velocity for the fall would not be 15 m/s.
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23.25 = 15dt + 5dt2
23.25 = 20dt3
dt = 1.047 s
10 m/s = (vf - 0 m/s) / 1.047s
Vf = 10.47 m/s
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• At what clock time(s) will the speed of the ball be 5 meters / second?
answer/question/discussion: ->->->->->->->->->->->-> :
10 m/s = (5 m/s - 0 m/s) / dt
Dt = .5 m/s
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I believe the first time the ball's speed is 5 m/s is 1 sec after being released. It reaches the same speed on the way down, and I believe that occurs 2 sec later. Check and see if I'm right.
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• At what clock time(s) will the ball be 20 meters above the ground?
• How high will it be at the end of the sixth second?
answer/question/discussion: ->->->->->->->->->->->-> :
20 m - 12 m = 8 m
Ds = v0 * dt + .5(a) * dt2
8 m = 15 m/s * dt + .5(-10m/s/s) *dt2
8 m = 15dt + -5dt2
8 m = 10dt3
Dt = .928 s
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Pretty good, but not all your results are correct so be sure to check both my notes and the discusison at the link.
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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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