With the table at hand, you are now ready to fill it in.
The baseball is thrown straight UP at a speed of 20 m/s. Gravity causes it to slow down at a rate of 10 m/s/s. At one second the ball is traveling 10 m/s slower than it was initially. So, the velocity at 1 second is 10 m/s UP.
The average velocity of the ball in the first second is (20 m/s UP + 10 m/s UP)/2 or 15 m/s UP. The ball travels 15 m UP in the first second. Fill in "15 m ABOVE Cliff" in the Height column.
The one second row in your table should now read:
In the second second, the baseball slows down an additional 10 m/s. At 2 seconds its velocity is zero.
The average velocity between one and two seconds is (10 m/s UP + 0)/2 or 5 m/s UP. The ball goes an additional 5 m UP during the second second. Adding this to the 15 m UP traveled in the first second, we find that the ball is now 20 m ABOVE the cliff.
The two second row in your table should look like:
The ball begins to move DOWN after two seconds.
At three seconds the baseball is traveling 10 m/s faster DOWN than at two seconds. Since the speed at two seconds was zero, the velocity at three seconds is 10 m/s DOWN.
During this third second, the average velocity of the ball is (0 + 10 m/s DOWN)/2 or 5 m/s DOWN. Thus, the ball travels 5 m DOWN from its highest point of 20 m ABOVE the cliff at the two second mark. Enter 15 m ABOVE Cliff in the Height column.
The three second row in the table should now be filled in as follows.
When the time of flight is four seconds the velocity of the basball is 20 m/s DOWN. The average speed betwen three and four seconds is (10 m/s DOWN + 20 m/s DOWN)/2 or 15 m/s. This means that the ball traveled 15 m DOWN between the three and four second marks. Since the ball was 15 m ABOVE the cliff at three seconds, the basball is once again at cliff height. Enter "At Cliff Height" in your table under the Height column. (In case you're wondering, it was great if you guessed this one. This is the symmetry we talked about in class.)
Your table should now have a four second row that looks like this:
At five seconds the ball gains yet another 10 m/s, so that the ball's velocity is 30 m/s DOWN. The average velocity in the fifth second is (20 m/s DOWN + 30 m/s DOWN)/2 or 25 m/s DOWN. And, the ball travels 25 m DOWN between four and five seconds. Since the ball was at cliff height at the four second mark, you enter "25 m BELOW Cliff" in the Height Column. Now, your table should have a row that looks like the one below.
In the sixth, and final second, the baseball picks up one more 10 m/s of speed. At six seconds the ball's velocity is 40 m/s DOWN. The average velocity in the sixth second is (30 m/s DOWN + 40 m/s DOWN)/2 or 35 m/s DOWN. That means that the ball falls another 35 m DOWN. Adding this to the 25 m BELOW the cloff the ball was at five seconds, you enter "60 m BELOW Cliff" in the Height column. Your final row now looks like the one below.
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