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PHY 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: ->->->->->->->->->->->-> :
vf = v0 + a('dt),
(vf - v0) / a = 'dt,
(0 m/s - 15 m/s) / (-10 m/s^2) = 'dt
1.5 s = 'dt.
'ds = (vf + v0)/2 * 'dt
'ds = (0 m/s + 15 m/s)/2 * 1.5s,
'ds = 11.25 m
12 m + 11.25 m = 23.25 m above 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: ->->->->->->->->->->->-> :
'ds = (v0 * 'dt) + (.5 * aAve * 'dt^2),
-23.25 m = (0 m/s * 'dt) + (.5 * (-10 m/s^2) * 'dt^2),
-23.25 m = -5 m/s^2 * 'dt^2,
+-sqrt(4.65 s^2) = 'dt,
+- 2.156 s = 'dt,
2.156 s + 1.5 s = 3.66 seconds.
vf = v0 + aAve * 'dt,
vf = 0 - 10 m/s^2 * 2.156 s
vf = -21.56 m/s
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At what clock time(s) will the speed of the ball be 5 meters /
second?
answer/question/discussion: ->->->->->->->->->->->-> :
vf = v0 + aAve * 'dt,
(vf - v0) / aAve = 'dt,
(5 m/s - 15 m/s) / -10 m/s^2 = 'dt,
1 second = 'dt
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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: ->->->->->->->->->->->-> :
'ds = 20 m - 12 m = 8 meters,
going up the vAve is 7.5 m/s,
'ds = vAve * 'dt,
'ds / vAve = 'dt,
8 m / 7.5 m/s = 'dt,
1.07 seconds = 'dt to reach 20 meters above the ground.
vf = v0 + aAve * 'dt
vf = 0 m/s + (-10 m/s^2) * 6 S
vf = -60 m/s,
'ds = (vf + v0)/2 * 'dt,
'ds = (-60 m/s + 0 m/s)/2 * 6 s,
'ds = -180 m,
12 m - 180 m = 168 m below the starting point.
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*#&!
@& Good. No need for revision but check the discussion at the links.
&#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
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