Why are there two answers to (b)?

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In summary, a stone is thrown vertically upward with a speed of 24.0 m/s. When it reaches a height of 13.0 m/s, it is moving at a speed of 24.0 m/s. It takes approximately 1.5 seconds to reach this height. There are two answers to this question because the stone reaches this height twice during its trajectory, once on the way up and once on the way down. This is due to the fact that what goes up must come down, unless the object exceeds escape velocity.
  • #1
hitemup
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Homework Statement



A stone is thrown vertically upward with a speed of 24.0 m/s.

a) How fast is it moving when it reaches a height of 13.0 m/s?
b) How much time is required to reach this height?
c) Why are there two answers to (b)?

Homework Equations


[/B]
x = v0t +- 1/2 at2

The Attempt at a Solution



I had no problem with the first two, but I've thought I need an explanation for the third one. Here is the graph and solutions. Does the second root appear because of the stone's falling right after reaching its maximum height?

http://www4c.wolframalpha.com/Calculate/MSP/MSP42811iec8be4feb3fd0e00001afd1ed1gd449fc6?MSPStoreType=image/gif&s=16&w=86.&h=18. http://www4c.wolframalpha.com/Calculate/MSP/MSP42841iec8be4feb3fd0e00003d457bh4d7i14gi8?MSPStoreType=image/gif&s=16&w=78.&h=18.
http://www4c.wolframalpha.com/Calculate/MSP/MSP42881iec8be4feb3fd0e0000509big5995b3732e?MSPStoreType=image/gif&s=16&w=392.&h=192.&cdf=Coordinates&cdf=Tooltips
 
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  • #2
That's right. What goes up must come down!

It passes the 13m level twice. In fact, it passes through every level twice, except for the point at the very apex of the trajectory.
 
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  • #3
NascentOxygen said:
What goes up must come down!
Unless it exceeds escape velocity :D
 

Related to Why are there two answers to (b)?

1. Why are there two answers to (b)?

There may be two answers to (b) because the problem is asking for a possible solution or outcome. This means that there could be more than one correct answer based on different approaches or interpretations of the problem.

2. Can both answers to (b) be correct?

Yes, both answers to (b) can be correct. As mentioned, there could be multiple solutions or outcomes that are considered correct for the problem at hand.

3. How do I know which answer to choose?

The choice of answer may depend on the specific context or purpose of the problem. It is important to carefully read the instructions or consider the given information to determine which answer is most appropriate.

4. Are there any guidelines for choosing between the two answers?

There may be some guidelines or criteria provided in the problem to help you choose between the two answers. These could include factors such as efficiency, accuracy, or relevance to the problem.

5. Can I get credit for either answer in an exam or assignment?

In most cases, you should be able to receive credit for either answer in an exam or assignment as long as it is a valid and logical solution to the problem. However, it is always best to clarify with your instructor or refer to the grading rubric for specific guidelines.

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