cq_1_082

Phy 231

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: ->->->->->->->->->->->-> :

+ 15 m/s and – 10 m/s^2

-15 m/s / -10 m/s = 1.5 m/s

(15 m/s + 0 m/s)/2 = 7.5 m/s is the vAve

7.5 m/s * 1.5 m/s = 11.25 meters

highest point is therefore 12 meters + 11.25 meters = 23.25 meters

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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: ->->->->->->->->->->->-> :

v0 = + 15 m/s, vf = ?

I am going to use the equation: vf ^2 = v0^2 + 2 * a * ds

vf^2 = 15^2 + 2 * (-10) * (-12)

vf^2 = 225 +240

vf = sqrt(465)

vf = -+21.56 m/s but it has to be – because of the conditions and common sense

vf = - 21.56

(-21.56 m/s + 15 m/s)/2 = -3.28 m/s is the vAve

vAve = ds/dt to find dt

-3.28m/s = -12 m/ dt which is 3.66 seconds

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• At what clock time(s) will the speed of the ball be 5 meters / second?

answer/question/discussion: ->->->->->->->->->->->-> :

The ball will be 5 m/s at:

(5 m/s - 15 m/s) = -10 m/s

-10 m/s / -10 m/s = 1 second

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• At what clock time(s) will the ball be 20 meters above the ground?

20 meters = (vf – v0)/dt

since the ball started at 12 meters high, the change in velocity needs to be 8 meters. The given initial velocity is 15 m/s.

vf^2 = v0^2 + 2 * a * ds

vf = sqrt(15 m/s^2 + 2 * (-10 m/s^2) * 8 m)

vf = sqrt(65 m^2/s^2)

vf = +- 8.06

(-8.06 m/s – 15 m/s)/ (-10 m/s) = 2.31 s is the time the bal will be 20 meters above the ground.

• How high will it be at the end of the sixth second?

answer/question/discussion: ->->->->->->->->->->->-> :

It will end up below 0 so the acceleration doesn’t really affect the ball anymore so there is no need to determine it.

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35 minutes

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