# Very simple gravity/time/distance travelled problem

• dkayuk
In summary, the conversation is about calculating the time it takes for a droplet of water to fall from point A to point B, and then from point X to point B. The formula t1 = √(2d/g) can be used to calculate the time for the first distance, but a different method is needed for the second distance as the droplet already has a certain speed. By subtracting the time it takes for the droplet to reach point X (t[X]) from the time it takes to reach point B (t[1]), the time for the second distance (t2) can be calculated. This information is being sought for high speed photography purposes.
dkayuk

## Homework Statement

This isn't really homework, because I'm not at school anymore (aged 42!) but I will describe as best as I can.

A small object like a droplet of water is released from a height (point A), falling on the surface (Point B) with initial speed 0. Distance between A and B, I will call d and obviously there's gravity (g) and time it takes for the droplet to fall from A to B, I will call t1. I know the equation so that given d is known, and so is gravity, then I can calculate time (t1).

Suppose that between points A and B, there's a point X. By the time the droplet has reached X is already has a certain speed. How do I calculate the time (t2) that it takes for the droplet to travel from X to the surface (B)?

## Homework Equations

t1=square_root((2 * d)/g)

## The Attempt at a Solution

I know (or at least I think I know) that I can't use the same equation to calculate t2 because the droplet already has a certain speed.

Apologies, if I'm not explaining this very well. I've not done any physics for 25 years and the reason I need this is because I'm doing high speed photography with falling objects.

thx

DK

If you know the distance AX, you can use the above equation to calculate the time for the droplet to reach point X, t[X]. As t[1] stays the same whether or not you add an extra reference point, simply substract t[X] from t[1] and you have your answer.

Hope this helps.

I can provide a response to your question. In order to calculate the time (t2) it takes for the droplet to travel from X to the surface (B), we can use the equation for constant acceleration: v = u + at, where v is final velocity, u is initial velocity, a is acceleration, and t is time. In this case, we can assume that the acceleration is constant due to gravity.

First, we need to calculate the initial velocity (u) of the droplet at point X. This can be done using the equation for distance: s = ut + 1/2at^2, where s is distance, u is initial velocity, a is acceleration, and t is time. We know the distance (d) between points A and X, and we can assume that the initial velocity at point A is 0. Therefore, we can solve for u, which will give us the initial velocity at point X.

Once we have the initial velocity (u), we can use the equation v = u + at to solve for t2. We know that the final velocity (v) at point B is 0, so we can plug in the values for u, a (gravity), and v into the equation and solve for t2.

I hope this helps and good luck with your high speed photography!

## 1. What is the formula for calculating the distance travelled with simple gravity and time?

The formula for calculating distance travelled with simple gravity and time is d = 1/2 * gt^2, where d is the distance, g is the acceleration due to gravity, and t is the time.

## 2. How does mass affect the distance travelled in a simple gravity and time problem?

In a simple gravity and time problem, mass does not affect the distance travelled. The distance travelled is solely dependent on the acceleration due to gravity and the time elapsed.

## 3. Can the formula be used for objects with different accelerations due to gravity?

Yes, the formula can be used for objects with different accelerations due to gravity. However, the value of g should be substituted with the appropriate value for the specific object or location.

## 4. How do you calculate the time elapsed in a simple gravity and distance travelled problem?

The formula for calculating time elapsed in a simple gravity and distance travelled problem is t = √(2d/g), where t is the time, d is the distance, and g is the acceleration due to gravity.

## 5. Is this formula applicable to objects with initial velocities?

Yes, this formula is applicable to objects with initial velocities. However, the initial velocity should be taken into account and added to the final velocity in the calculation for distance travelled.

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