Question
constant speed of 3 fts . When the worker’s arms are 10 ft off the ground, her coworker throws a measuring tape toward her. The measuring tape is thrown from a height of 6 ft with an initial vertical velocity of
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COMPLETE
The sy]jtem has no real solutions. What does this indicate about the worker’s arms and the measuring tape?
They will never be at the same height at the same time.
They will be at the same height exactly once.
They will be at the same height at two different times.
v
COMPLETE
The sy]jtem has no real solutions. What does this indicate about the worker’s arms and the measuring tape?
They will never be at the same height at the same time.
They will be at the same height exactly once.
They will be at the same height at two different times.
Ask by Mccoy Wyatt. in the United States
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
They will never be at the same height at the same time.
Solution
To determine the relationship between the height of the worker’s arms and the height of the measuring tape over time, we need to analyze the two equations given:
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The height of the worker’s arms as a function of time:
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The height of the measuring tape as a function of time:
We need to find the values of
Let’s rearrange this equation to set it to zero:
Now, we can simplify this equation:
Next, we will use the discriminant to determine the nature of the solutions. The discriminant
where
Calculating the discriminant:
Since the discriminant is negative (
Conclusion:
The absence of real solutions means that the worker’s arms and the measuring tape will never be at the same height at the same time. Thus, the correct interpretation is:
They will never be at the same height at the same time.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
When analyzing the motion of the worker’s arms and the thrown measuring tape, it’s fascinating to see how both objects move through space. Since the problem yields no real solutions, this tells us that mathematically, the worker’s arms and the tape will never align in height. In simpler terms, as the worker reaches up with her arms, the measuring tape begins to fall too quickly for them to ever be at the same height.
In practical terms, this is like trying to catch a balloon that’s just too high up, no matter how much you stretch your arms or jump. It’s a great reminder of the importance of timing and trajectory in projectiles – sometimes objects can seem close but due to speed and path, they are perfectly out of reach! Always aim carefully!
