Phy 121
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: ->->->->->->->->->->->-> : 25 m/s – 10 m/s = 15 m/s
• What will be its velocity at the end of two seconds?
answer/question/discussion: ->->->->->->->->->->->-> : 15 m/s – 10 m/s = 5 m/s
• During the first two seconds, what therefore is its average velocity?
answer/question/discussion: ->->->->->->->->->->->-> : (15 m/s + 5 m/s) / 2 = 10 m/s
• How far does it therefore rise in the first two seconds?
answer/question/discussion: ->->->->->->->->->->->-> : 10 m/s * 2 s = 20 m
• What will be its velocity at the end of a additional second, and at the end of one more additional second?
answer/question/discussion: ->->->->->->->->->->->-> : 5 m/s – 10 m/s = -5 m/s; -5 m/s – 10 m/s = -15 m/s
• At what instant does the ball reach its maximum height, and how high has it risen by that instant?
answer/question/discussion: ->->->->->->->->->->->-> : After 2.5 seconds at a height of 31.25 meters
v0 = 25 m/s, vf = 0 m/s, a = -10 m/s^2, t = ?, `ds = ?
vf = v0 + a * `dt
(vf – v0) / a = `dt
`dt = (0 m/s – 25 m/s) / -10 m/s^2
`dt = -25 m/s / -10 m/s^2 = 2.5 sec
Vf^2 = v0^2 + 2a`ds
Vf^2 – v0^2 = 2a`ds
`ds = (vf^2 – v0^2) / 2a
`ds = [(0 m/s)^2 – (25 m/s)^2] / 2 * -10 m/s^2
`ds = -625 m^2/s^2 / -20 m/s^2
`ds = 31.25 m
• 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: ->->->->->->->->->->->-> : 5 m/s; 20 m
`dt = 4 s
V0 = 25 m/s
A = -10 m/s
Vf = v0 + a * `dt
Vf = 25 m/s + -10 m/s^2 * 4 s
Vf = 25 m/s + -40 m/s
Vf = -15 m/s
vAve = (vf – v0) / 2
vAve = (-15 m/s + 25 m/s) / 2
vAve = 5 m/s
`ds = vAve * `dt
`ds = 5 m/s * 4 s
`ds = 20 m
• How high will it be at the end of the sixth second?
answer/question/discussion: ->->->->->->->->->->->-> : 30 meters below the initial point
`dt = 6 s
V0 = 25 m/s
A = -10 m/s
Vf = v0 + a * `dt
Vf = 25 m/s + -10 m/s^2 * 6 s
Vf = 25 m/s + -60 m/s
Vf = -35 m/s
vAve = (vf – v0) / 2
vAve = (-35 m/s + 25 m/s) / 2
vAve = -5 m/s
`ds = vAve * `dt
`ds = -5 m/s * 6 s
`ds = -30 m
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30 minutes
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&#Good responses. See my notes and let me know if you have questions. &#