PHY 121
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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: ->->->->->->->->->->->-> :
vf = v0 + a * ‘dt
vf = 25 m/s + -10 m/s^2 * 1 s
vf = 25 m/s + -10 m/s^2
vf = 15 m/s
• What will be its velocity at the end of two seconds?
answer/question/discussion: ->->->->->->->->->->->-> :
vf = v0 + a * ‘dt
vf = 25 m/s + -10 m/s^2 * 2s
vf = 25 m/s + -20 m/s^2
vf = 5 m/s
• During the first two seconds, what therefore is its average velocity?
answer/question/discussion: ->->->->->->->->->->->-> :
vAve = (v0 + vf) /2
vAve = (25 m/s + 5 m/s) /2
vAve = 30 m/s / 2
vAve = 15 m/s
• How far does it therefore rise in the first two seconds?
answer/question/discussion: ->->->->->->->->->->->-> :
y = v^2 – v0^2 / 2 a
y = (5 m/s)^2 – (25 m/s)^2 / 2(-10 m/s^2)
y = 25 m/s – 625 m/s / -20 m/s^2
y = -600 m/s / -20 m/s^2
y = 30 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: ->->->->->->->->->->->-> :
vf = v0 + a * ‘dt
vf = 25 m/s + 10 m/s^2 * 3 s
vf = 25 m/s + 30 m/s ^2
vf = 55 m/s
vf = v0 + a * ‘dt
vf = 25 m/s + 10 m/s^2 * 4 s
vf = 25 m/s + 40 m/s^2
vf = 65 m/s
• At what instant does the ball reach its maximum height, and how high has it risen by that instant?
answer/question/discussion: ->->->->->->->->->->->-> :
t = - v0/a
t = – 25 m/s / -10 m/s^2
t = 2.5 s
y = v^2 – v0^2 / 2 a
y = 0 - (25 m/s)^2 / 2(-10 m/s^2)
y = 0 – 625 m/s / -20 m/s^2
y = -625 m/s / -20 m/s^2
y = 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: ->->->->->->->->->->->-> :
vAve = (v0 + vf) /2
vAve = (25 m/s + -15 m/s) / 2
vAve = 10 m/s / 2
vAve = 5 m/s
y = v^2 – v0^2 / 2 a
y = - (-15 m/s)^2 – (25 m/s)^2 / 2(10 m/s^2)
y = -225 m/s – 625 m/s / -20 m/s^2
y = -850 m/s / -20 m/s^2
y = 42.5 m
• How high will it be at the end of the sixth second?
answer/question/discussion: ->->->->->->->->->->->-> :
vf = v0 + a * ‘dt
vf = 25 m/s + (-10 m/s^2) 6 s
vf = 25 m/s + -60 m/s^2
vf = -35 m/s
y = - v^2 – v0^2 / 2 a
y = - (-35 m/s)^2 – (25 m/s)^2 / 2(10 m/s^2)
y = -1225 m/s – 625 m/s / 20 m/s^2
y = -1850 m/s / 20 m/s^2
y = 3 m
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20 minutes
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Solution
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