# How long does it take a ball to be back

• mimi.janson
In summary, the conversation discusses finding the time it takes for a ball thrown vertically to reach its maximum height and return to its starting point. The formula for vertical motion is used to determine the initial upward velocity and acceleration due to gravity. It is concluded that the time it takes for the ball to stop moving up is the same amount of time it takes for it to come back down. Differentiation is not needed, and the time can be found by setting the formula for vertical motion equal to 0.
mimi.janson

## Homework Statement

A ball is trown vertically straight up in the air. After t seconds the ball has reached the higth

Question : after how many sconds is the ball back to the spot it was trown from ?

## Homework Equations

I have figured out that i need to differentate.

## The Attempt at a Solution

So i thought i had to solve it this was :

60t – 5t2 --> 60-10t but it seems like this isn't the answer

besides i have made a drawing of the information i got . The orange line shows how the ball is thrown straight up, and the blue shows that i have to solve how much that and the orange are when they are added when reffereing to time in seconds .

#### Attachments

• Unavngivet.png
810 bytes · Views: 420
Last edited:
mimi.janson said:

## Homework Statement

A ball is trown vertically straight up in the air. After t seconds the ball has reached the higth s(t) = 60t – 5t2 in metres

Question : after how many sconds is the ball back to the spot it was trown from ?

## Homework Equations

I have figured out that i need to differentate.

## The Attempt at a Solution

So i thought i had to solve it this was :

60t – 5t2 --> 60-10t but it seems like this isn't the answer

besides i have made a drawing of the information i got . The orange line shows how the ball is thrown straight up, and the blue shows that i have to solve how much that and the orange are when they are added when reffereing to time in seconds .

one formula for vertical motion is S = ut + 1/2 gt2 (acceleration under g)

By comparison to s(t) = 60t – 5t2

we can see the initial upward velocity is 60 m-1 and g is taken as 10 ms-2.

In that case you can easily establish how long it takes to stop moving up, and it takes that much again to come back down.

EDIT: you don't need differentiation - just find the values of t when S(t) = 0 - and one of those times is at time zero - when it all began.

PeterO said:
one formula for vertical motion is S = ut + 1/2 gt2 (acceleration under g)

By comparison to s(t) = 60t – 5t2

we can see the initial upward velocity is 60 m-1 and g is taken as 10 ms-2.

In that case you can easily establish how long it takes to stop moving up, and it takes that much again to come back down.

EDIT: you don't need differentiation - just find the values of t when S(t) = 0 - and one of those times is at time zero - when it all began.

ok thank you

## 1. How is the time it takes for a ball to be back calculated?

The time it takes for a ball to be back is calculated using the formula: t = √(2d/g), where t is time, d is the distance the ball is dropped from, and g is the acceleration due to gravity (9.8 m/s²).

## 2. Does the weight of the ball affect the time it takes for it to be back?

Yes, the weight of the ball does affect the time it takes for it to be back. The heavier the ball, the faster it will fall due to gravity, resulting in a shorter time for it to be back.

## 3. Is the air resistance considered in the calculation of the time for a ball to be back?

No, the calculation for the time it takes for a ball to be back assumes that there is no air resistance. In reality, air resistance can slow down the ball and affect the time it takes for it to be back.

## 4. Does the height from which the ball is dropped affect the time for it to be back?

Yes, the height from which the ball is dropped does affect the time it takes for it to be back. The higher the ball is dropped from, the longer it will take for it to be back due to the increased distance it has to travel.

## 5. Can the time for a ball to be back be different on different planets?

Yes, the time for a ball to be back can be different on different planets because the acceleration due to gravity varies from planet to planet. Therefore, the formula used to calculate the time will also be different, resulting in a different time for the ball to be back.

• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
34
Views
989
• Introductory Physics Homework Help
Replies
20
Views
2K
• Introductory Physics Homework Help
Replies
60
Views
924
• Introductory Physics Homework Help
Replies
32
Views
2K
• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
3K
• Introductory Physics Homework Help
Replies
9
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
20
Views
1K