determining the correct table for projectile motion\na ball is dropped from above ground level and hits the…
determining the correct table for projectile motion\na ball is dropped from above ground level and hits the ground sometime between 4 and 6 seconds after it is dropped. the balls height in meters is modeled by a function h(t), where t represents time in seconds. which table most likely relates to this function?\n| t | h(t) | | t | h(t) | | t | h(t) | | t | h(t) |\n| 0 | 70 | | 0 | 100 | | 0 | -150 | | 0 | 180 |\n| 2 | 50.4 | | 2 | 80.4 | | 2 | -130.4 | | 2 | 160.4 |\n| 4 | -8.4 | | 4 | 21.6 | | 4 | -71.6 | | 4 | 101.6 |\n| 6 | -106.4 | | 6 | -76.4 | | 6 | 26.4 | | 6 | 3.6 |
Answer
Explanation:
Step1: Analyze the physical situation
The ball is dropped from above ground - level, so at (t = 0), the height (h(0)>0). Also, as time passes and the ball falls, the height (h(t)) should decrease until it hits the ground ((h(t)=0)) between (t = 4) and (t = 6) seconds.
Step2: Check the first - row values
For (t = 0), the height should be positive. We can eliminate the table where (h(0)=- 150) since height above the ground cannot be negative at the start.
Step3: Check the decreasing nature
The height should decrease with time. In the first table, at (t = 4), (h(4)=-8.4) which means the ball is below the ground level before (t = 6) seconds which is not correct as it is supposed to hit the ground between (4) and (6) seconds. In the second table, (h(0) = 100), (h(2)=80.4), (h(4)=21.6), (h(6)=-76.4). The ball goes below the ground level at (t = 6) seconds which is consistent with hitting the ground between (4) and (6) seconds. In the fourth table, the height is still positive at (t = 6) seconds ((h(6)=3.6)), so it has not hit the ground yet.
Answer:
The second table (with (h(0) = 100), (h(2)=80.4), (h(4)=21.6), (h(6)=-76.4))