# Falling object and distance between time intervals

• Jakedidit
In summary, the distance (in meters) that the bowling ball falls during the interval between the 8th and 9th second can be calculated by finding the distance the ball falls in 8 seconds, then in 9 seconds, and subtracting the two values. If the distance at 9 seconds is over 324 meters, the ball will hit the ground between the 8th and 9th second, so the distance can be found by subtracting the distance at 8 seconds from 324 meters. The given equation d=4.9t^2 and gravity acceleration of 9.8 m/s^2 can be used in the calculations.
Jakedidit

## Homework Statement

Gravity on a falling object causes the object to descend a distance of d=4.9t^2, where d is the distance in meters and t is the time in seconds. A bowling bll is dropped from the top of the Eiffel Tower in Paris, France, which is 324 meters in height. If you neglect any type of air resistance, what is the distance (in meters) that the ball falls during the interval between the 8th and 9th second?

## Homework Equations

d=4.9t^2 is given;
Gravity acceleration is 9.8 m/s^2

## The Attempt at a Solution

Should we calculate the distance the bowling ball will fall in 8 seconds? then 9 seconds? then subtract the two? (Can't fall more than 324 meters)

Calculate how far it has fallen in 8 seconds. Then calculate how far it has fallen in 9 seconds.

If for example in 8 seconds it has fallen 200m and in 9 it has fallen 250m then the distance is 50m.

But if your distance at 9 seconds is over 324m then it will have hit the ball between the 8th and 9th second, so you will just take away the distance at the 8th second from 324.

Yes, that would be the correct approach. First, we can calculate the distance the ball falls in 8 seconds using the given equation d=4.9t^2, where t=8 seconds. This gives us a distance of d=313.6 meters. Then, we can calculate the distance the ball falls in 9 seconds using the same equation, but with t=9 seconds. This gives us a distance of d=441.9 meters.

To find the distance between the 8th and 9th second, we can subtract the distance at t=8 seconds from the distance at t=9 seconds. This gives us a distance of 441.9 - 313.6 = 128.3 meters. Therefore, the ball falls a distance of 128.3 meters during the interval between the 8th and 9th second.

It is important to note that this calculation assumes there is no air resistance, which may not be the case in real life. However, for the purpose of this problem, neglecting air resistance is a reasonable assumption.

## What is the formula for calculating the distance traveled by a falling object over a given time interval?

The formula for calculating the distance traveled by a falling object over a given time interval is d = 1/2gt^2, where d is the distance, g is the acceleration due to gravity (9.8 m/s^2), and t is the time interval.

## How does the mass of a falling object affect its distance traveled over a given time interval?

The mass of a falling object does not affect its distance traveled over a given time interval, as long as the object is subject to the same acceleration due to gravity. This is because the formula for distance traveled (d = 1/2gt^2) does not include mass as a variable.

## What is the relationship between the time interval and the distance traveled by a falling object?

The distance traveled by a falling object is directly proportional to the square of the time interval. This means that as the time interval increases, the distance traveled by the object also increases. For example, if the time interval is doubled, the distance traveled will be four times as much.

## How does air resistance affect the distance traveled by a falling object over a given time interval?

Air resistance can decrease the distance traveled by a falling object over a given time interval by slowing down its acceleration due to gravity. This is because air resistance creates a force that opposes the downward force of gravity, causing the object to fall at a slower rate. However, the effect of air resistance is typically negligible for smaller, denser objects.

## What is the difference between free fall and a falling object over a given time interval?

Free fall refers to the motion of an object that is only subject to the force of gravity. In this case, the object will accelerate at a constant rate of 9.8 m/s^2 and will not experience any other forces, such as air resistance. A falling object over a given time interval refers to an object that is subject to other forces, such as air resistance or a changing gravitational field, in addition to the force of gravity. This can result in a non-constant acceleration and different distance traveled over a given time interval.

Replies
3
Views
1K
Replies
5
Views
664
Replies
8
Views
11K
Replies
43
Views
2K
Replies
2
Views
2K
Replies
16
Views
3K
Replies
34
Views
1K
Replies
14
Views
2K
Replies
26
Views
6K
Replies
2
Views
1K