Question

a 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?

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, the height of the ball should decrease until it hits the ground (\(h(t)=0\)) between \(t = 4\) and \(t = 6\) seconds.

Step2: Check the first - value condition

Eliminate the table with \(h(0)= - 150\) since height cannot be negative at the start when it is dropped from above ground - level.

Step3: Check the height - decreasing condition

For the remaining tables, check if the height is decreasing over time.

• In the first table, at \(t = 4\), \(h(4)=-8.4\) which is not possible as height cannot be negative before hitting the ground.
• In the third table, at \(t = 6\), \(h(6)=-76.4\) which is not possible as height cannot be negative before hitting the ground.
• In the fourth table, \(h(0)=180\), \(h(2)=160.4\), \(h(4)=101.6\), \(h(6)=3.6\). The height is positive at \(t = 0\) and is decreasing over time and is close to \(0\) between \(t = 4\) and \(t = 6\) seconds.

Answer:

The fourth table (with \(t = 0,h(t)=180\); \(t = 2,h(t)=160.4\); \(t = 4,h(t)=101.6\); \(t = 6,h(t)=3.6\))