Throwing two stones, find the velocity of the second stone

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SUMMARY

The discussion revolves around a physics problem involving two stones, where the first stone is dropped from a height of 49 meters and the second stone is thrown after 1 second. Both stones hit the ground simultaneously, leading to confusion about the velocity of the second stone. The correct approach involves using the equations of motion: h = 1/2gt² for the first stone and h = 1/2a(t-1)² for the second stone. The final conclusion is that the initial velocity of the second stone is indeed 12 m/s, as stated in the book, and the confusion stemmed from misunderstanding the relationship between acceleration and initial velocity.

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Homework Statement


A man let a stone from height 49 metres. After 1 second he threw a second stone. Both stones fell on same time. What is the velocity of second stone?

Homework Equations


h=1/2gt^2
h=1/2a(t-1)^2

The Attempt at a Solution


So I assume that if he let the first stone then the acceleration is g

The second stone is thrown which means that his acceleration isn't g but a

I solved from equation h=1/2gt^2 the time and placed it into the next equation h=1/2a.(t-1)^2

I solved acceleration and put it into this equation v^2 = 2.a.s

I think the answer should be 45m/s but the answer in the book is 12m/s. How is this possible? Even the first stone won't fall with velocity 12m/s or am I wrong ?

I appreciate your help. Thank you
 
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HAF said:
The second stone is thrown which means that his acceleration isn't g but a
Why? Does the acceleration depend on the velocity in this case? Assume no air resistance.
HAF said:
h=1/2a(t-1)^2
Doesn't the second stone have some initial velocity that you are trying to find?
 
kuruman said:
Why? Does the acceleration depend on the velocity in this case? Assume no air resistance.

Doesn't the second stone have some initial velocity that you are trying to find?
Why? Because I think that it's acceleration has to be greater than g because the second stone will "catch" the first one.

There is nothing written there about initial velocity.
 
HAF said:
Why? Because I think that it's acceleration has to be greater than g because the second stone will "catch" the first one.
Do you really believe that objects in free fall have different accelerations depending on ... what? If someone shoots a bullet straight down, will the bullet have an even larger acceleration? So according to you an object will have acceleration g only if it released from rest? I think you are conflating acceleration and velocity.
 
kuruman said:
Do you really believe that objects in free fall have different accelerations depending on ... what? If someone shoots a bullet straight down, will the bullet have an even larger acceleration? So according to you an object will have acceleration g only if it released from rest? I think you are conflating acceleration and velocity.
Wait a second please. I'm confused.

My current opinion is that a shooted bullet has to have greater acceleration because it will fall down faster than an object which was released from rest.

Bullet is in my opinion pushed by the gun thus he has to have greater acceleration.

Please can you correct me?
 
HAF said:
Bullet is in my opinion pushed by the gun thus he has to have greater acceleration.
If the bullet is pushed by the gun, it has a higher initial velocity but not a higher acceleration. That is at the heart of your confusion. Think about it for a while before replying.
 
Remember Newton... F=ma...so for there to be an acceleration there must be a force. When does the man/gun apply a force on the object? Before or after it leaves his hand/gun?
 
CWatters said:
Remember Newton... F=ma...so for there to be an acceleration there must be a force. When does the man/gun apply a force on the object? Before or after it leaves his hand/gun?
Man/gun applies force during the interaction or am I wrong?
 
HAF said:
Man/gun applies force during the interaction or am I wrong?
Yes, but the interaction pretty much ceases after the bullet leaves the muzzle. So what is the acceleration subsequently?
 
  • #10
HAF said:
There is nothing written there about initial velocity.
It is not clear to me whether the question is asking for the initial velocity or the final velocity, but my guess would be that they want the initial one.
Have you quoted the question exactly as given to you?
 
  • #11
haruspex said:
It is not clear to me whether the question is asking for the initial velocity or the final velocity, but my guess would be that they want the initial one.
Have you quoted the question exactly as given to you?
Yeah It should be initial velocity. My bad.
 
  • #12
I solved it thank you very very much! And sorry for being anoying
 

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