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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.
** 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: ->->->->->->->->->->->-> :
a=(vf-v0)/'dt
-10m/s^2=(0-15m/s)/'dt
'dt=-15m/s/-10m/s^2
'dt=1.5s
vAve=(0m/s+15m/s)/2
vAve=7.5m/s
vAve='ds/'dt
7.5m/s*1.5s='ds
11.25='ds
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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: ->->->->->->->->->->->-> :
vf^2 = ( v0^2 + 2 a `ds)
vf^2= (15 m/s)^2 + 2 * (-10 m/s^2) * (-12 m)
vf^2=225 m^2/s^2 + 240 m^2/s^2
sqrt(vf^2)= sqrt(465 m^2/s^2)
vf= +-21.56 m/s
vAve = (+15 m/s + -21.6 m/s ) / 2 = -3.3 m/s
`dt = `ds / vAve = -12 m / (-3.3 m/s) = 3.6 sec
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At what clock time(s) will the speed of the ball be 5 meters / second?
answer/question/discussion: ->->->->->->->->->->->-> :
a='dv/'dt
-10m/s^2*'dt=(5m/s-15m/s)
'dt=(5m/s-15m/s)/-10m/s^2
'dt= 1s
a='dv/'dt
-10m/s^2*'dt=(-5m/s-15m/s)
'dt=(5m/s-15m/s)/-10m/s^2
'dt=2s
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At what clock time(s) will the ball be 20 meters above the ground?
answer/question/discussion: ->->->->->->->->->->->-> :
vf^2 = v0^2 + 2 a `ds
vf^2 = v0^2 + 2 a `ds
vf^2= (15 m/s)^2 + 2 * (-10 m/s^2) * 8 m
sqrt(vf^2)= sqrt( 65 m^2 / s^2)
vf= +-8.1 m/s
`dt = (vf - v0) / a
'dt= (8.1 m/s - 15 m/s) / (-10 m/s^2)
'dt= .69 s
`dt = (vf - v0) / a
'dt= (-8.1 m/s - 15 m/s) / (-10 m/s^2)
'dt= 2.31 s.
How high will it be at the end of the sixth second?
answer/question/discussion: ->->->->->->->->->->->-> :
vf=15 cm/s + (-10 m/s^2) * 6 s
vf= -45 m/s.
vAve=(15 m/s + (-45 m/s) ) / 2
vAve = -15 m/s
vAve='ds/'dt
vAve*'dt='ds
-15 m/s * 6 s
'ds= - 90 m.
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45
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&#Very good work. Let me know if you have questions. &#