Subjects algebra

Ball Height Bf2C6B

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1. **Problem Statement:** Determine which statement about the ball's motion is not true based on the graph of height vs. time. 2. **Given Information:** The graph is a downward-opening parabola representing height $h(t)$ in feet over time $t$ in seconds. - The ball starts at height 0 at $t=0$. - The ball reaches a maximum height around 45 feet at $t=4$ seconds. - The ball returns to height 0 at about $t=8$ seconds. 3. **Analyze each statement:** - Statement 1: "The ball is in the air for 8 seconds." - The ball starts at $t=0$ and lands at $t=8$ seconds, so total air time is 8 seconds. - This statement is **true**. - Statement 2: "The ball is at the same height at 3 seconds and at 5 seconds." - Since the parabola is symmetric about $t=4$, heights at $t=3$ and $t=5$ are equal. - This statement is **true**. - Statement 3: "The ball reaches a maximum height of 40 feet." - The graph shows the maximum height is about 45 feet, not 40. - This statement is **not true**. - Statement 4: "The ball takes the same amount of time to go up as it takes to come down." - The parabola is symmetric, so time to reach max height (4 seconds) equals time to fall back down (4 seconds). - This statement is **true**. 4. **Conclusion:** The statement that is not true is: "The ball reaches a maximum height of 40 feet."