cq_1_181

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phy121

Your 'cq_1_18.1' 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 child in a slowly moving car tosses a ball upward. It rises to a point below the roof of the car and falls back down, at which point the child catches it. During this time the car neither speeds up nor slows down, and does not change direction.

• What force(s) act on the ball between the instant of its release and the instant at which it is caught? You can ignore air resistance.

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

friction and gravity

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• What happens to the speed of the ball between release and catch? Describe in some detail; a graph of speed vs. clock time would also be appropriate.

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

As the ball rises, the speed will decrease until it reaches its highest point, where the speed will be zero. As it comes back down, the speed increases. On a graph of speed vs clock time, the vertical direction is changing but the horizontal is constant. You can see that the speed decreases at first until zero then increases back up, and make the graph look like a U or an inverted parabola.

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• Describe the path of the ball as it would be observed by someone standing along the side of the road.

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

With someone watching, they will see the ball go straight up and straight down. There will be no horizontal movement.

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The car is moving past someone standing on teh side of the road. They would therefore see the ball moving forward (and in fact would experience this if they got in the way of the ball, which of course would be hard to do as the ball is in the car, but you will get my point) as well as up and down.

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• How would the path differ if the child was coasting along on a bicycle? What if the kid didn't bother to catch the ball? (You know nothing about what happens after the ball makes contact with the ground, so there's no point in addressing anything that might happen after that point).

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

The path would not differ if the bike was travelling at the same speed, but if the child did not catch the ball, the balls distance would increase.

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• What if the child drops the ball from the (inside) roof of the car to the floor? For the interval between roof and floor, how will the speed of the ball change? What will be the acceleration of the ball? (You know nothing about what happens after the ball makes contact with the floor, so there's no point in addressing anything that might happen after that point).

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

the force of gravity is 9.8m/s^2, which means that the ball would accelerate at the speed. Depending on the distance the ball travels, the speed would change.

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• What if the child holds the ball out of an open window and drops it. If the ball is dense (e.g., a steel ball) and the car isn't moving very fast, air resistance will have little effect. Describe the motion of the ball as seen by the child. Describe the motion of the ball as seen by an observer by the side of the road. (You know nothing about what happens after the ball makes contact with the ground, so there's no point in addressing anything that might happen after that point).

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

As the car is moving horizontally, the child will see the ball move horizontally along the car and drop straight down. The bystander would see the ball move forward with the speed of the car.

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20 minutes

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A child in a car tosses a ball upward so that after release it requires 1/2 second to rise and fall back into the child's hand at the same height from which it was released. The car is traveling at a constant speed of 10 meters / second in the horizontal direction.

• Between release and catch, how far did the ball travel in the horizontal direction?

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

the ball continues to travel at 10m/s in the horizontal direction, therefore

‘ds= vAve*’dt

‘ds= 10m/s*0.5s

‘ds= 5m

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• As observed by a passenger in the car, what was the path of the ball from its release until the instant it was caught?

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

the observer will see the ball as if it is curved.

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An observer in the car doesn't see the child moving forward, nor does he see the car moving forward. Objects which are stationary outside the car will appear to be moving backward.

The ball will appear to travel striaght up and down.

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This will no longer be the case if the car accelerations while the ball is in the air.

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• Sketch the path of the ball as observed by a line of people standing along the side of the road. Describe your sketch. What was shape of the path of the ball?

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

The path of the ball is curved upwards.

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The ball would travel upward for awhile, but its observed path will be a parabola which opens downward.

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• How fast was the ball moving in the vertical direction at the instant of release? At that instant, what is its velocity as observed by a line of people standing along the side of the road?

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

-9.8m/s^2*0.5s= -4.9m/s

Therefore the initial velocity would be 2.45m/s

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• How high did the ball rise above its point of release before it began to fall back down?

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

‘ds= vAve*’dt

‘ds= 1.23m/s*.25s

‘ds= 0.31m

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20 minutes

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&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.

Then please compare your old and new solutions with the expanded discussion at the link

Solution

Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.

If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#

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Good overall, but perhaps there are a couple of misconceptions in some of your answers.

Check the notes I've inserted, as well as the discussion below. I believe you'll understand everything, so there is no need for any revision unless you feel the need.

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