Phy 201
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A ball rolls off the end of an incline with a vertical velocity of 20 cm/s downward, and a horizontal velocity of 80 cm/s. The ball falls freely to the floor 120 cm below.
• For the interval between the end of the ramp and the floor, hat are the ball's initial velocity, displacement and acceleration in the vertical direction?
v0 = 20 cm/s
`ds = 120 cm
a = 980 cm/s/s
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• What therefore are its final velocity, displacement, change in velocity and average velocity in the vertical direction?
vf = 0 cm/s
`ds = 120 cm
`dv = -20 cm/s
vAve = 10 cm/s
Accelerating uniformly downward at 980 cm/s^2, the final velocity during the uniform-acceleration interval is not 0 cm/s. This may occur after the acceleration changes due to contact with the floor, but that's not part of the uniform acceleration interval.
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• What are the ball's acceleration and initial velocity in the horizontal direction, and what is the change in clock time, during this interval?
v0 = 80 cm/s
vAve = `ds / `dt
10 cm/s = 120 cm / `dt
`dt = 12s
vf = v0 + a * `dt
0 cm/s = 80 cm/s + a * 12s
-80 cm/s = a * 12s
a = -6.67 cm/s/s
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• What therefore are its displacement, final velocity, average velocity and change in velocity in the horizontal direction during this interval?
vf = 0 cm/s
vAve = 40 cm/s
`dv = -80 cm/s
vAve = `ds * `dt
40 cm/s = `ds / 12s
`ds = 480 cm
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• After the instant of impact with the floor, can we expect that the ball will be uniformly accelerated?
No.
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• Why does this analysis stop at the instant of impact with the floor?
It is uncertain how the ball will react after hitting the floor.
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10 minutes
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Solution
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