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Phy 121
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Random prob Week 4 Quiz 2
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An object is given an unknown initial velocity up a long ramp on which its acceleration is known to have magnitude 12 cm/s^2. .198 seconds later it passes a point 7.5 cm up the ramp from its initial position.
• What are its possible initial velocities, and what is a possible scenario for each?
• What is the maximum distance the object travels up the ramp?
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I am lost on what to do, this is a hard problem. This is what I have so far:
I used 'ds=v0* 'dt+1/2(a)*('dt)^2
7.5 cm=v0*0.198 s+1/2(12 cm/s^2)*(0.198s)^2
v0=17.31 cm/s^2
I am stuck after that, could you go through this with me?
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You have a great start. However since the object is traveling up the ramp, its acceleration and its velocity will be in opposite directions.
The first this you need to do is declare the positive direction. That can be up the ramp, in which case the initial velocity and displacement will be positive and acceleration negative, or down the ramp, in which case initial velocity and displacement will be negative and acceleration positive.
That will slightly change the magnitude of your initial velocity.
The next question regards the max distance up the ramp. You have the initial velocity and the acceleration, so to answer this question you only have to notice that the maximum distance will occur when the velocity reaches zero.
Another question that often arises is when the ball again reaches the 7.5 cm position. You can use the initial velocity and acceleration, along with `ds = 7.5 cm, to answer this question. The equation you get will be quadratic in `dt, so you will have two possible solutions.
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