#$&*
PHY 121
Your 'cq_1_18.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
A child in a slowly moving car tosses a ball upward. It rises to a point below the roof of the car and falls back down, at which point the child catches it. During this time the car neither speeds up nor slows down, and does not change direction.
What force(s) act on the ball between the instant of its release and the instant at which it is caught? You can ignore air resistance.
answer/question/discussion: ->->->->->->->->->->->-> n:
gravity acts through the entire interval with no other forces present
#$&*
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: ->->->->->->->->->->->-> n:
From release, the speed of the ball will begin to decrease as gravity is doing negative work against the ball. At the instant the ball reaches its apex, the ball’s speed will briefly equal zero and then the ball will begin accelerating back toward the child until caught. Both the acceleration and deceleration due to gravity will be constant
#$&*
Describe the path of the ball as it would be observed by someone standing along the side of the road.
answer/question/discussion: ->->->->->->->->->->->-> n:
It would appear to arc forward as it rises and falls
#$&*
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: ->->->->->->->->->->->-> n:
I think this would depend on the speed of the bicycle. If it is great enough, I believe air resistance would cause the ball to appear to again arc, but this time backwards. If you are not traveling very fast, it would act this same. If the ball is not caught, everything would be the same, just more greatly exaggerated.
#$&*
What if the child drops the ball from the (inside) roof of the car to the floor? For the interval between roof and floor, how will the speed of the ball change? What will be the acceleration of the ball? (You know nothing about what happens after the ball makes contact with the floor, so there's no point in addressing anything that might happen after that point).
answer/question/discussion: ->->->->->->->->->->->-> n:
The ball’s velocity will increase from acceleration due to gravity at a constant rate.
#$&*
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: ->->->->->->->->->->->-> n:
I think without air resistance, that the circumstances would not change. It would appear to drop straight down for the child, and arc for the observer.
#$&*
** **
25m
** **
child in a car tosses a ball upward so that after release it requires 1/2 second to rise and fall back into the child's hand at the same height from which it was released. The car is traveling at a constant speed of 10 meters / second in the horizontal direction.
Between release and catch, how far did the ball travel in the horizontal direction?
answer/question/discussion: ->->->->->->->->->->->-> :
v = 10m/sec
`dt = .5sec
`ds = 10m/sec*.5sec
=5m
#$&*
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 ball will arc caused by decreasing velocity as the ball moves up and increasing velocity as it moves down.
#$&*
Sketch the path of the ball as observed by a line of people standing along the side of the road. Describe your sketch. What was shape of the path of the ball?
answer/question/discussion: ->->->->->->->->->->->-> :
It would begin at the child’s hand and arc upward eventually coming to the point when the ball ceases to move vertically. It would then begin to arc downward until rest. The shape is similar to a parabola though not as symmetrical I suppose.
#$&*
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: ->->->->->->->->->->->-> :
`ds = 0m
a = -9.8m/sec
`dt = .5sec
`ds = v0*`dt + .5(a*`dt^2)
0m = v0* .5sec + .5(-9.8m/sec^2*(.5sec^2))
0m = v0*.5sec + -1.225m
1.225m = v0+.5sec
V0 = 2.45m/sec
#$&*
How high did the ball rise above its point of release before it began to fall back down?
answer/question/discussion: ->->->->->->->->->->->-> n:
v0 = 2.45m/sec
vf = 0m/sec
a = -9.8m/sec
`dt = .5sec*(.5) = .25sec
`ds = (2.45m/sec+0m/sec)/2 * .25sec
`ds = .31m
#$&*
*#&!*#&!
&#Very good responses. Let me know if you have questions. &#