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Phy 121
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** CQ_1_13.1_labelMessages **
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, what are the ball's initial velocity, displacement and acceleration in the vertical direction?
The initial velocity is the horizontal velocity of 80cm/s. The displacement is 120cm, the acceleration is 9.8m/s^2.
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80 cm/s isn't in the vertical direction.
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What therefore are its final velocity, displacement, change in velocity and average velocity in the vertical direction?
We find the final velocity by
Vf = `sqrt [(0.8m/s)^2 + 2 (9.8m/s^2)(12m)]
= 0.64m^2/s^2 + 235.2m^2/s^2
= `sqrt 235.84m^2/s^2
Fv = 15.4 m/s
The average velocity is the average of the initial and final velocities or 8.1m/s.
The displacement of 12m divided by the average velocity of 8.1m/s gives a time interval of 1.5s.
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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?
The acceleration in the horizontal direction is 0. The initial velocity like we said before is 0.8m/s. The change in clock time is 1.5s.
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What therefore are its displacement, final velocity, average velocity and change in velocity in the horizontal direction during this interval?
I dont know how to relate these two quantities. A different vertical and horizontal velocity
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Motion in the horizontal direction is independent of motion in the vertical direction. The only thing they share is the time interval.
Confining your attention just to the horizontal quantities, where you know the acceleration and intial velocity, as well as the time interval, what are your answers to these questions?
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After the instant of impact with the floor, can we expect that the ball will be uniformly accelerated?
The ball will not be accelerated at all because it is on the floor not moving.
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You don't know what the floor is made of, or the ball, so you don't know what happens to the ball when it hits the floor.
However the one thing you do know is that the acceleration is going to change. The analysis has assumed uniform acceleration, and that assumption is no longer valid when the ball contacts the floor.
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Why does this analysis stop at the instant of impact with the floor?
All forces and accelerations reach 0 at this point so the object stops moving.
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