the table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds…
the table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds after it is thrown upward.\nwhich statements are true? check all that apply.\nthe ball is at the same height as the building between 8 and 10 seconds after it is thrown.\nthe height of the ball decreases and then increases.\nthe ball reaches its maximum height about 4 seconds after it is thrown.\nthe ball hits the ground between 8 and 10 seconds after it is thrown.\nthe height of the building is 81.6 meters.\n|t|h(t)|\n|0|0|\n|2|60.4|\n|4|81.6|\n|6|63.6|\n|8|6.4|\n|10|-90|\n|12|-225.6|
Answer
Explanation:
Step1: Analyze height at start
At $t = 0$, $h(0)=0$. This is the starting - point (roof of the building).
Step2: Observe height changes
The height $h(t)$ first increases from $h(0) = 0$ to $h(4)=81.6$ and then decreases.
Step3: Check maximum - height time
The height is maximum at $t = 4$ seconds with $h(4)=81.6$ meters.
Step4: Analyze hitting the ground
The height is positive at $t = 8$ ($h(8)=6.4$) and negative at $t = 10$ ($h(10)= - 90$). So the ball hits the ground between 8 and 10 seconds.
Step5: Check building height
The building height is $h(0) = 0$ (the reference point), not 81.6 meters.
Answer:
The ball reaches its maximum height about 4 seconds after it is thrown. The ball hits the ground between 8 and 10 seconds after it is thrown.