At what speed must I throw vertically an object.

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To determine the initial speed required for an object to lose 25% of its speed in the first second, the final speed must be expressed as 0.75 times the initial speed. The equation V final = V initial + a * t, with acceleration as -9.8 m/s², is used to relate the speeds. The correct approach involves substituting V final with 0.75 * V initial and rearranging the equation to solve for V initial. The discussion highlights the importance of correctly expressing the relationship between initial and final speeds to arrive at the solution.
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Homework Statement


At what speed must I throw vertically an object so that it will lose 25 % of its speed during the first second.

Homework Equations


V final = v initial + a * t

The Attempt at a Solution



v final * 0.75 = v initial + -9.8 m/s^2 * 1 second

That's pretty much what I figured out only ...
 
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astrololo said:
only ...
"Only,..." what?
 
Bystander said:
"Only,..." what?
Is there a problem ?
 
You haven't answered the original question, what's the original vertical speed?
 
Bystander said:
You haven't answered the original question, what's the original vertical speed?
Well that's the thing I have no idea of how to obtain the answwer...
 
You're interested in the rate at which the object loses speed, and specifically asked for a 25% loss in one second. What's "vfinal" for 100% loss?
 
Bystander said:
You're interested in the rate at which the object loses speed, and specifically asked for a 25% loss in one second. What's "vfinal" for 100% loss?
Well it's 0.
 
astrololo said:
V final = v initial + a * t
Substitute that value, and rearrange. What's "v(t=1s)" relative to "vinitial?"
 
Bystander said:
Substitute that value, and rearrange. What's "v(t=1s)" relative to "vinitial?"
Vi=9,8 m/s
 
  • #10
What's "a?"
 
  • #11
Bystander said:
What's "a?"
-9.8 m/s^2
 
  • #12
9.8 is what percentage of 9.8?
 
  • #13
Bystander said:
9.8 is what percentage of 9.8?
100%
 
  • #14
In one second, the speed changes by how much?
 
  • #15
Bystander said:
In one second, the speed changes by how much?
it goes from 9.8 to 0.
 
  • #16
astrololo said:
it goes from 9.8 to 0.
No. It changes by 9.8.
 
  • #17
Bystander said:
No. It changes by 9.8.
Yes, that's what I said. ok, it changes by 9.8.
 
  • #18
astrololo said:
v final * 0.75 = v initial + -9.8 m/s^2 * 1 second
Fix the left hand side of that equation. Then you should be able to solve for vinitial.
 
  • #19
Doc Al said:
Fix the left hand side of that equation. Then you should be able to solve for vinitial.
I put it that way so that the speed would be 75%... it's not correct?
 
  • #20
astrololo said:
I put it that way so that the speed would be 75%... it's not correct?
No, it's not correct.

This is the formula you are trying to use:
astrololo said:
V final = v initial + a * t

Hint: express Vfinal in terms of Vinitial.
 
  • #21
Doc Al said:
No, it's not correct.

This is the formula you are trying to use:Hint: express Vfinal in terms of Vinitial.
v initial = Vfinal/(a * t)

Vinitial = V final / (-9.8* 1)

Vinitial = V final / -9.8

This is what you want ?
 
  • #22
astrololo said:
This is what you want ?
No. I want you to fix the left hand side of your equation, just like I asked.

First step: Can you tell me what's wrong with it?
 
  • #23
Doc Al said:
No. I want you to fix the left hand side of your equation, just like I asked.

First step: Can you tell me what's wrong with it?
Well I multiplied the left side by 75%
So we have v final = v initial + a* t
 
  • #24
astrololo said:
Well I multiplied the left side by 75%
So we have v final = v initial + a* t
But the left side of your equation was 0.75vfinal, not vfinal. Fix that!
 
  • #25
Doc Al said:
But the left side of your equation was 0.75vfinal, not vfinal. Fix that!
Ok, so I had v final * 0.75 = v initial + -9.8 m/s^2 * 1 second

and I change it to v final = v initial + -9.8 m/s^2 * 1 second
 
  • #26
astrololo said:
Ok, so I had v final * 0.75 = v initial + -9.8 m/s^2 * 1 second

and I change it to v final = v initial + -9.8 m/s^2 * 1 second
Good. Now express vfinal in terms of vinitial. (That's where the 0.75 comes in.) That way you can solve for vinitial.
 
  • #27
Doc Al said:
Good. Now express vfinal in terms of vinitial. (That's where the 0.75 comes in.) That way you can solve for vinitial.
So we have Vf + 9.8 = Vi

I will multiply Vf by 0.75 ?
 
  • #28
astrololo said:
So we have Vf + 9.8 = Vi

I will multiply Vf by 0.75 ?
No. First things first. Forget about that equation for a moment.

Express vfinal in terms of vinitial. Once you get that correct, then you can go back to the equation.
 
  • #29
Doc Al said:
No. First things first. Forget about that equation for a moment.

Express vfinal in terms of vinitial. Once you get that correct, then you can go back to the equation.
Sorry, english isn't my first language. You mean that you want V final in function of Vinitial, right ? Like what we had with v final = v initial + -9.8 m/s^2 * 1 second
 
  • #30
astrololo said:
Sorry, english isn't my first language. You mean that you want V final in function of Vinitial, right ? Like what we had with v final = v initial + -9.8 m/s^2 * 1 second
Forget about that equation for the moment. What I want you to do is express this fact:
astrololo said:
that it will lose 25 % of its speed during the first second.

Then you can combine that with the other equation.
 
  • #31
Doc Al said:
Forget about that equation for the moment. What I want you to do is express this fact:Then you can combine that with the other equation.
Ok, so you want this

v final = v initial + -9.8 m/s^2 * 1 second
AND
v final * 0.75 = v initial + -9.8 m/s^2 * 1 second

*I have a feeling that you're not going to be happy.
 
  • #32
astrololo said:
Ok, so you want this

v final = v initial + -9.8 m/s^2 * 1 second
This one's good. Put it aside for now.

astrololo said:
AND
v final * 0.75 = v initial + -9.8 m/s^2 * 1 second
This one's plain wrong. Realize that this one contradicts the previous one. Toss it out.

astrololo said:
*I have a feeling that you're not going to be happy.
Not yet. :wink:

Hint: Is vfinal ten times bigger than vinitial? Would you write: vfinal = 10vinitial?

How would you write their relative size?
 
  • #33
Doc Al said:
This one's good. Put it aside for now.This one's plain wrong. Realize that this one contradicts the previous one. Toss it out.Not yet. :wink:

Hint: Is vfinal ten times bigger than vinitial? Would you write: vfinal = 10vinitial?

How would you write their relative size?
No, we actually know that the object is going to lose 25 % of its speed after 1 second.
 
  • #34
astrololo said:
No, we actually know that the object is going to lose 25 % of its speed after 1 second.
Exactly. Now express that mathematically: vfinal = ?vinitial.
 
  • #35
Doc Al said:
Exactly. Now express that mathematically: vfinal = ?vinitial.
vfinal = 0.75 * vinitial

In this case, we are saying that the initial speed is going to lose 25 %, which makes us say that the final speed is going to be equal to 0.75 * vinitial because the final speed is the moment where we lost 25 %
 
  • #36
astrololo said:
vfinal = 0.75 * vinitial
Exactly!

Now combine that with your other equation to eliminate vfinal. Then you can solve for vinitial.
 
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  • #37
Doc Al said:
Exactly!

Now combine that with your other equation to eliminate vfinal. Then you can solve for vinitial.
WOW. How could I have been such an idiot. We know that our final is going to be 25 less than the initial speed. What smart idea do I bring ? Take 75 % of 75% of V initial. I have been been taking 75 % TWO times. Anyway, thank you for your help and patience !
 

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