Phy 201
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.
** **
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: ->->->->->->->->->->->-> :
Gravity and physical manipulation.
#$&*
What happens to the speed of the ball between release and catch? Describe in some detail; a graph of speed vs. clock time would also be appropriate.
answer/question/discussion: ->->->->->->->->->->->-> :
The speed of the ball from release to its highest point will slow down and then stop for a brief instant. It will speed up as it falls from its highest point, until it is caught. A graph of speed vs. clock time would look like a u that is resting on the x-axis.
#$&*
Describe the path of the ball as it would be observed by someone standing along the side of the road.
answer/question/discussion: ->->->->->->->->->->->-> :
Someone standing along the side of the road, would observe the ball going up and back down, in relatively the same position.
#$&*
How would the path differ if the child was coasting along on a bicycle? What if the kid didn't bother to catch the ball? (You know nothing about what happens after the ball makes contact with the ground, so there's no point in addressing anything that might happen after that point).
answer/question/discussion: ->->->->->->->->->->->-> :
If the child was coasting along on a bicycle, on the balls descent back down to be caught, it would be significantly closer to the child, if not hitting them. If the child didnt bother to catch the ball, depending on the angle it was thrown up at, it would either hit the bicycle, the child, or the ground directly, but in any case it would end up on the ground.
#$&*
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 speed of the ball as it falls from the roof to the floor will increase. The acceleration of the ball is that of gravity (9.8 m/s/s).
#$&*
What if the child holds the ball out of an open window and drops it. If the ball is dense (e.g., a steel ball) and the car isn't moving very fast, air resistance will have little effect. Describe the motion of the ball as seen by the child. Describe the motion of the ball as seen by an observer by the side of the road. (You know nothing about what happens after the ball makes contact with the ground, so there's no point in addressing anything that might happen after that point).
answer/question/discussion: ->->->->->->->->->->->-> :
As seen by the child, the ball will appear to drop fairly vertically, with slight horizontal movement towards the rear of the car. To an observer by the side of the road, the ball will appear to drop vertically and a bit more horizontal movement to the rear of the car will be able to be detected.
#$&*
** **
30 minutes
** **
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: ->->->->->->->->->->->-> :
vAve = 10 m/s
`dt = .5 sec
`ds = vAve * `dt
`ds = 10 m/s * .5 sec
`ds = 5 m
The ball traveled 5 meters because that is how much the car moved in that time period.
#$&*
As observed by a passenger in the car, what was the path of the ball from its release until the instant it was caught?
answer/question/discussion: ->->->->->->->->->->->-> :
It would appear to go up and back down in relatively the same position.
#$&*
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: ->->->->->->->->->->->-> :
By a line of people along the side of the road, it would appear to go straight up and down inside the car. But since the car is moving forward, it would also have moved forward 5 meters in the time frame.
#$&*
How fast was the ball moving in the vertical direction at the instant of release? At that instant, what is its velocity as observed by a line of people standing along the side of the road?
answer/question/discussion: ->->->->->->->->->->->-> :
vf = v0 + a * `dt
0 m/s = v0 + -9.8 m/s/s * .25 sec
0 m/s = v0 2.45 m/s
v0 = 2.45 m/s
To a line of people standing along the side of the road, it would probably appear much faster.
#$&*
How high did the ball rise above its point of release before it began to fall back down?
answer/question/discussion: ->->->->->->->->->->->-> :
vAve = (2.45 m/s + 0 m/s) / 2
vAve = 1.23 m/s
`ds = vAve * `dt
`ds = 1.23 m/s * .25s
`ds = .31 m
#$&*
** **
20 minutes
** **
Most answers are good but you do have a couple of misconceptions, more likely misreadings. Be sure to read the discussions at the given links. No need for revision unless you have questions.
&#Please compare your 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. &#
&#Please compare your 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. &#