Dennis and Carmen problem with my trial solution , is it right?

  • Thread starter nareeman
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In summary: Exactly! And what about the ball thrown downward with the same initial velocity X? When it gets to the same point on its way down, what is its velocity at that point?the same initial velocity X as wellThat's right! So both balls will have the same velocity at that point, making their final speed the same when they hit the ground.
  • #1
nareeman
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Homework Statement



Dennis and Carmen are standing on the edge of a cliff. Dennis throws a basketball vertically upward, and at the same time Carmen throws a basketball vertically downward with the same initial speed. You are standing below the cliff observing this strange behavior. Whose ball is moving fastest when it hits the ground?

Homework Equations



v^2 = v0^2 -2gΔy


The Attempt at a Solution


in the same speed cause when Dennis basketball back to the initial position "`the throwing position" it will back with the same initial speed with different direction "the same direction as Carmen" so it's the same but it'll take Dennis basketball more time
Dennis
v0 is +
v^2 =+v0^2 -2gΔy
Carmen
v0 is -
v^2 =-v0^2 -2gΔy
-----
g =-9.8 for both
Δy is the same for both


so
Dennis v^2 =+v0^2
Carmen v^2 =-v0^2
add them
v^2+v^2 =0

v^2 =-v^2

please tell me if that's right if not how it can be solve
thank you:smile:
 
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  • #2
nareeman said:

Homework Statement



Dennis and Carmen are standing on the edge of a cliff. Dennis throws a basketball vertically upward, and at the same time Carmen throws a basketball vertically downward with the same initial speed. You are standing below the cliff observing this strange behavior. Whose ball is moving fastest when it hits the ground?

Homework Equations



v^2 = v0^2 -2gΔy


The Attempt at a Solution


in the same speed cause when Dennis basketball back to the initial position "`the throwing position" it will back with the same initial speed with different direction "the same direction as Carmen" so it's the same but it'll take Dennis basketball more time
Your logic is correct :approve:

Dennis
v0 is +
v^2 =+v0^2 -2gΔy
Carmen
v0 is -
v^2 =-v0^2 -2gΔy
Careful, the formula wants you to square the initial velocity. Carmen's initial velocity is -v0, and squared is (-v0)(-v0) = +v02.

As you can see, the initial velocity being negative does not change the result.

-----
g =-9.8 for both
Δy is the same for both


so
Dennis v^2 =+v0^2
Carmen v^2 =-v0^2
add them
v^2+v^2 =0

v^2 =-v^2
If you consider that last line of math it represents an impossible situation, since you can't have any real number squared that turns out negative. The glitch can be traced back to squaring the initial velocity as I pointed out above.

You could also have used a conservation of energy approach (if you've covered that yet in your course).
 
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  • #3
thank you ,we have not cover it yet
so if I'm going to answer for that question in the exam i just write this formula "v^2 = v0^2 -2gΔy" and say
everything is the same for both cases " v0^2 -2gΔy"
then the final speed is the same
only or should i add something else ?
 
  • #4
nareeman said:
thank you ,we have not cover it yet
so if I'm going to answer for that question in the exam i just write this formula "v^2 = v0^2 -2gΔy" and say
everything is the same for both cases " v0^2 -2gΔy"
then the final speed is the same
only or should i add something else ?

Forget the math for a minute and just think about it this way. If the ball thrown upward has an initial velocity X, then when it gets back to the same point on its way down, what is its velocity at that point?
 
  • #5
nareeman said:
thank you ,we have not cover it yet
so if I'm going to answer for that question in the exam i just write this formula "v^2 = v0^2 -2gΔy" and say
everything is the same for both cases " v0^2 -2gΔy"
then the final speed is the same
only or should i add something else ?

That's all you really need :smile:
 
  • #6
phinds said:
Forget the math for a minute and just think about it this way. If the ball thrown upward has an initial velocity X, then when it gets back to the same point on its way down, what is its velocity at that point?

the same initial velocity that was it thrown with
 

What is the "Dennis and Carmen problem"?

The "Dennis and Carmen problem" refers to a specific scientific problem or issue that Dennis and Carmen are facing in their research or experiment.

What is the trial solution and why is it important?

The trial solution is a proposed solution or hypothesis that is being tested in an experiment. It is important because it allows researchers to gather data and evaluate whether or not the solution is effective.

How do I know if my trial solution is right?

There are a few factors to consider when evaluating the effectiveness of a trial solution. These include the data and results collected, the control group used for comparison, and the relevance and accuracy of the solution to the problem at hand.

What should I do if my trial solution is not working?

If your trial solution is not producing the desired results, it is important to re-evaluate and make any necessary adjustments. This could involve changing variables, modifying the method or approach, or seeking input and advice from other scientists.

How can I improve my trial solution?

To improve your trial solution, it is important to constantly analyze and interpret the data collected and make adjustments as needed. Seeking feedback from other scientists and conducting further research can also help in refining and improving the solution.

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