# Throwing two stones, find the velocity of the second stone

• HAF
In summary, a man dropped a stone from a height of 49 metres and threw a second stone after 1 second. Both stones fell at the same time. The question is asking for the velocity of the second stone. The equations used were h=1/2gt^2 and h=1/2a(t-1)^2, and the resulting acceleration was used in the equation v^2 = 2.a.s. The confusion arose from the belief that an object's acceleration depends on its initial velocity, but in reality, the acceleration remains constant in free fall. The correct answer is 12m/s, and the question was referring to the initial velocity of the second stone.
HAF

## 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?

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

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.

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?

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?

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.

I solved it thank you very very much! And sorry for being anoying

## 1. What is the equation for calculating the velocity of the second stone?

The equation for calculating the velocity of the second stone is v2 = v1 + (g * t), where v2 is the velocity of the second stone, v1 is the initial velocity of the first stone, g is the acceleration due to gravity, and t is the time interval between the two stones being thrown.

## 2. How do you measure the time interval between the two stones being thrown?

The time interval between the two stones being thrown can be measured using a stopwatch or a timer. The stopwatch should be started as soon as the first stone is released and stopped as soon as the second stone is released.

## 3. What is the value of acceleration due to gravity?

The value of acceleration due to gravity is approximately 9.8 m/s^2 on Earth. However, this value may vary slightly depending on location and altitude.

## 4. Can the velocity of the second stone be greater than the first stone?

Yes, the velocity of the second stone can be greater than the first stone if the second stone is thrown with a greater initial velocity or if the time interval between the two throws is longer.

## 5. How does air resistance affect the velocity of the second stone?

Air resistance can decrease the velocity of the second stone as it travels through the air. This is because the air resistance exerts a force in the opposite direction of the stone's motion, causing it to slow down. However, the effect of air resistance may be negligible for short distances and low velocities.

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