Your 'cq_1_18.2' 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 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?
The ball traveled for half a second in a car that travels 10m/sec. That means that the ball traveled 5 meters.
answer/question/discussion:
• As observed by a passenger in the car, what was the path of the ball from its release until the instant it was caught?
The ball appeared to go straight up and straight back down into the boy’s hand. In reality it went the same horizontal speed and direction of the car.
Good answer, but relative to the roadside the ball travels at a constant horizontal velocity while rising more and more slowly, then falling more and more quickly. This gives it a curved path within that frame of reference. In fact it can (and will) be shown that the path would be parabolic, for the present a good description would indicate a curved path, increasing at a decreasing rate then decreasing at an increasing rate.
think about the following:
There is no universal fixed frame of reference, and if there was it wouldn't be the surface of the spinning, orbiting Earth at the time and location of these events. So while the meaning of your answer is clear, the phrase 'in reality' is not appropriate. It would not be inappropriate to say that 'relative to the roadside it traveles with the same horizontal speed and direction of the car, while in the vertical direction it accelerated first upward then downward'.
answer/question/discussion:
• 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?
The ball’s distance becomes greater and greater.
This is not a description of a shape. See my preceding note.
answer/question/discussion:
• 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?
There is a relationship that states that the ball’s vertical velocity will be the horizontal velocity squared. So the vertical velocity will be 25m/sec
I don't know of any such relationship. There is however a square proportionality between vertical distance fallen and horizontal distance traveled.
You are given the time required to rise and fall back into the child's hand. This allows you to find the initial and final vertical velocities.
As you observe, the horizontal velocity is constant.
answer/question/discussion:
• How high did the ball rise above its point of release before it began to fall back down?
The ball went up for the same amount of time that it went down. This means that at a vertical velocity of 25m/sec. Take a fourth of that to see how high the ball went. In this case it is 6.25m
A ball with initial vertical velocity 25 cm/s will rise for about 2.5 seconds at an average speed of 12.5 cm/s, rising a total of about 31 meters.
There is no rule that says you can take 1/4 of the initial vertical velocity to find the height to which the ball rises. 1/4 of a velocity is not in any case a displacement (different units, different definitions).
See my previous notes.
answer/question/discussion:
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5 minutes
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You need to make a few corrections on this problem.
&#Please see my notes and submit a copy of this document with revisions and/or questions, and mark your insertions with &&&&. &#