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Phy 121
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.
** CQ_1_08.2_labelMessages **
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: ->->->->->->->->->->->-> :
After one second the ball will move 15 meters from 12 meters to 27 meters, while at the same time the velocity of 15m/s decreases by 10m/s to 5m/s. The next second the ball goes 5m/s from 27 meters to 32 meters, while simultaneously decreasing its velocity by another 10 m/s to -5m/s. At 32 meters the ball is at its highest point. From here the velocity changes downwardly starting at -5m/s and decreasing by 10m/s every second until the ball hits the ground.
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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: ->->->->->->->->->->->-> :
If we go by what I have above, from its highest point the ball after one second decreases by 5 meters to 27 meters, while the velocity simultaneously decreases by 10 sec to -15m/s. The next second the ball will fall by 15 meters bringing it to 12 meters, while the velocity increases (notice I said INCREASE!!!) to -25m/s. The next second the ball will hit the ground so the ball is moving at 25m/s when it hits the ground.
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The speed increased, the magnitude of the velocity increased, but the velocity decreased. When you go from, say, -5 of something to -15 of the same thing, that thing decreases.
Your last statement
'The next second the ball will hit the ground so the ball is moving at 25m/s when it hits the ground.'
is correct. The ball is moving at 25 m/s, which means that its speed is 25 m/s. It is moving at 25 m/s in the negative direction, of course, so its velocity is -25 m/s.
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• At what clock time(s) will the speed of the ball be 5 meters / second?
answer/question/discussion: ->->->->->->->->->->->-> :
after one second the ball will have gone from an initial velocity of 15m/s to 5m/s.
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Right.
Also, in another second its velocity will be -5 m/s, so its speed will again be 5 m/s.
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• At what clock time(s) will the ball be 20 meters above the ground?
About 0.6 seconds. After one second the ball moves to 27 meters so I just kind of estimated here.
• How high will it be at the end of the sixth second?
answer/question/discussion: ->->->->->->->->->->->-> :
I can reason this all out in my head like I did on the first two problems, but I know there is a simpler method for doing so, and that direct reasoning will serve me less the more complex problems become. I will review the material for this assignment and see what I learn. The main hold up is the negative numbers and such. Velocity INCREASES to a negative number based on the acceleration of gravity, which for some reason because of the way the graph is set up is NOT negative. Normally when we talk about acceleration making an object decrease in velocity its like -2m/s^2, but that wouldn’t apply to the ball.. or would it? The ball is going up in a positive direction and the acceleration is pulling it down which would make acceleration negative, but you don’t have it annotated -10m/s^2 so im really not sure. I’ll wait for feedback and submit revisions if you wish.
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You can choose either direction to be positive. If you choose up as positive then since acceleration is downward, acceleration is negative. If you choose down as positive then acceleration is positive but the initial velocity, which is upward, is negative.
For the purpose of this exercise:
Remember that a negative quantity which approaches zero is increasing, a positive quantity which approaches zero is decreasing, and if a negative quantity has increasing magnitude it is decreasing.
If we choose up as positive, as we implicitly have in the preceding, the initial velocity is positive, acceleration is negative, velocity reaches zero after 2.5 seconds until which it is positive and its speed and velocity are both decreasing, velocity becomes negative after 2.5 seconds after which speed increases and velocity decreases.
If we choose down as positive, which is an equally valid choice, the initial velocity is negative, acceleration is positive, velocity reaches zero after 2.5 seconds until which it is negative and its speed is decreasing while its velocity is increasing, velocity becomes positive after 2.5 seconds after which speed and velocity both increase.
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Overall you're doing really well with this.
The signs and the increasing/decreasing behaviors of speed, velocity, position and acceleration are at first confusing. I've inserted a number of notes to hopefully help you sort out these ideas.
No need for a revision unless you have questions, but check out the discussion at
&#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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