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Answer :
To determine when Jerald is less than 104 feet above the ground after jumping from a bungee tower, we need to consider a logical approach to the problem.
1. Understanding the Problem:
- Jerald's height as a function of time (h) is modeled by some equation. Without the specific equation provided, we assume a quadratic function often used in physics for projectile or bungee motion: [tex]\( h(t) = -a \cdot t^2 + b \cdot t + c \)[/tex].
- Our task is to find when his height is less than 104 feet.
2. Analyzing the Intervals:
- We are given multiple intervals to consider:
- [tex]\( t > 6.25 \)[/tex]
- [tex]\( -6.25 < t < 6.25 \)[/tex]
- [tex]\( t < 6.25 \)[/tex]
- [tex]\( 0 \leq t \leq 6.25 \)[/tex]
3. Identifying when h < 104:
- Since the graph of a quadratic function can open upwards or downwards, typically with bungee jumping it opens downward.
- In a bungee jump, the height decreases to a minimum and then increases again. The critical part is from the initial jump until he bounces back above 104 feet.
- We're interested in the initial phase of descent after the jump and prior to that bounce above 104 feet.
4. Determining the Appropriate Interval:
- Based on logical reasoning:
- The interval [tex]\( -6.25 < t < 6.25 \)[/tex] suggests a symmetrical behavior about a reference point often considering negative "pre-launch" time which isn’t physically meaningful for this scenario.
- The interval [tex]\( 0 \leq t \leq 6.25 \)[/tex] captures the time frame starting from the jump until potentially when he rebounds to a height less than 104 feet.
Therefore, the correct interval for which Jerald's height is less than 104 feet is [tex]\( 0 \leq t \leq 6.25 \)[/tex]. This interval captures the descent from the jump until he potentially rebounds back upward.
1. Understanding the Problem:
- Jerald's height as a function of time (h) is modeled by some equation. Without the specific equation provided, we assume a quadratic function often used in physics for projectile or bungee motion: [tex]\( h(t) = -a \cdot t^2 + b \cdot t + c \)[/tex].
- Our task is to find when his height is less than 104 feet.
2. Analyzing the Intervals:
- We are given multiple intervals to consider:
- [tex]\( t > 6.25 \)[/tex]
- [tex]\( -6.25 < t < 6.25 \)[/tex]
- [tex]\( t < 6.25 \)[/tex]
- [tex]\( 0 \leq t \leq 6.25 \)[/tex]
3. Identifying when h < 104:
- Since the graph of a quadratic function can open upwards or downwards, typically with bungee jumping it opens downward.
- In a bungee jump, the height decreases to a minimum and then increases again. The critical part is from the initial jump until he bounces back above 104 feet.
- We're interested in the initial phase of descent after the jump and prior to that bounce above 104 feet.
4. Determining the Appropriate Interval:
- Based on logical reasoning:
- The interval [tex]\( -6.25 < t < 6.25 \)[/tex] suggests a symmetrical behavior about a reference point often considering negative "pre-launch" time which isn’t physically meaningful for this scenario.
- The interval [tex]\( 0 \leq t \leq 6.25 \)[/tex] captures the time frame starting from the jump until potentially when he rebounds to a height less than 104 feet.
Therefore, the correct interval for which Jerald's height is less than 104 feet is [tex]\( 0 \leq t \leq 6.25 \)[/tex]. This interval captures the descent from the jump until he potentially rebounds back upward.
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