# Solving a Free-Fall Problem with Height & Time

• lolrelativity
That gives you one equation to solve for T.In summary, to find the time and height of an object falling a distance h from rest, you can use the equation y=vt+.5gt^2 and solve for h and t using the given information. However, if the object travels a distance of 0.57h meters in the last 1 second, you will need to use additional equations and information to accurately solve for the time and height.
lolrelativity
I am wondering if I did this right.

## Homework Statement

An object falls a distance h from rest. If it travels 0.57h meters in the last 1.00 s,
I need to know the time and the height of its fall.

## The Attempt at a Solution

Here what I have:

Since it traveled .57H meters in the last second, I used y=vt+.5gt^2, and got .57H=4.9 since the time elapsed is 1 second and it came from rest, so the inital velocity is zero. Then I solved for H, getting around 8.59 m. Then with this I set up 8.59=4.9t^2, and solved for T, getting around 1.325 seconds. Was these the right methods?

Since, as you say, the initial velocity is 0, the distance traveled in t seconds is y= .5gt^2. But he "time elapsed" is NOT 1 second. You are told that the object travels 0.57h m in the last second but you don't know how many seconds it had fallen before that. You are assuming the object fell .57h m in the first second.

Suppose it fell for a total of T seconds. Then it fell .57h meters between T-1 and T. In the first T-1 seconds it fell .5g(T-1)^2 and in all T seconds it fell .5gT^2 meters. During that last second, it fell .5gT^2- .5g(T-1)^2= .57h meters. And, of course, you have .5gT^2= h, the total distance fallen.

Your solution looks correct! You correctly used the kinematic equation for position (y) to solve for the height (H) and time (t). You also used the appropriate initial conditions (initial velocity = 0 m/s) and correctly identified the acceleration due to gravity (g = 9.8 m/s^2). Your final answers for H and t also seem reasonable. Good job!

## What is a free-fall problem?

A free-fall problem is a type of physics problem where an object is dropped from a certain height and its motion is affected only by the force of gravity.

## What information do I need to solve a free-fall problem?

To solve a free-fall problem, you will need to know the initial height of the object, the time it takes to fall, and the acceleration due to gravity (usually given as 9.8 m/s²).

## How do I calculate the final height of an object in a free-fall problem?

The final height of an object in a free-fall problem can be calculated using the equation: h = h0 + v0t + (1/2)at², where h0 is the initial height, v0 is the initial velocity (usually 0 m/s), t is the time, and a is the acceleration due to gravity.

## What is the formula for calculating the time it takes for an object to fall in a free-fall problem?

The formula for calculating the time it takes for an object to fall in a free-fall problem is t = √(2h/a), where h is the initial height and a is the acceleration due to gravity. This assumes that the initial velocity is 0 m/s.

## Can I use the same formula to solve a free-fall problem on different planets or moons?

No, the formula for solving a free-fall problem only applies on Earth. The acceleration due to gravity varies on different planets and moons, so you will need to use a different formula for each one.

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