# Calculating a ratio in Free Fall motion

• vAhmed
In summary, you attempted to solve for v2 at y=h/2 and y=0 by setting v1 equal to 9.81 m/s and v2 equal to 4.9 m/s. You then attempted to solve for v2 at y=0 by dividing by v1. However, this does not seem to work because you cannot find an equation that relates displacement and speed that includes the acceleration.
vAhmed

## Homework Statement

A ball is thrown upward with a speed v 1. The ball reaches a maximum height of y=h. What is the ratio of the speed of the ball,v 2 , at y=h/2, to the initial upward speed of the ball,v 1 , at y=0?

## Homework Equations

I attached a picture.

We are currently studying the four equations for motions in a straight line.

## The Attempt at a Solution

I know that the acceleration would be constant as a = -g = -9.81m/s^2. And as the ball moves upward the acceleration will slow down the ball due to gravity. The ball was thrown meaning that v1≠ 0. So I set v1 = 9.81 m/s, and v2 = 9.81/2 = 4.9 m/s. Then V2/V1 equals 4.9/9.8 = 0.50. Although I think it doesn't make sense to divide 9.81 by 2. At this point, I couldn't do any better.

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vAhmed said:
I tried to calculate the velocity at y=0 to divide it by the velocity at y=h/2 but couldn't do it. I also thought of substituting or using imaginary values.
You seen to have removed the template where you were asked to show your work and show applicable equations.

We cannot tell what you have tried unless you tell us.

jbriggs444 said:
You seen to have removed the template where you were asked to show your work and show applicable equations.

We cannot tell what you have tried unless you tell us.
Sorry for that, I posted another thread.

vAhmed said:
I tried to calculate the velocity at y = 0 and y = h/2 but I couldn't. I also thought about substituting imaginary values.
It's not just the template you need. You need to show your work. Tell us what things you have tried. Not just the fact that they've failed.

Last edited:
CWatters
vAhmed said:

## Homework Statement

A ball is thrown upward with a speed v 1. The ball reaches a maximum height of y=h. What is the ratio of the speed of the ball,v 2 , at y=h/2, to the initial upward speed of the ball,v 1 , at y=0?

## Homework Equations

I attached a picture.
View attachment 231564
We are currently studying the four equations for motions in a straight line.

## The Attempt at a Solution

I know that the acceleration would be constant as a = -g = -9.81m/s^2. And as the ball moves upward the acceleration will slow down the ball due to gravity. The ball was thrown meaning that v1≠ 0. So I set v1 = 9.81 m/s, and v2 = 9.81/2 = 4.9 m/s. Then V2/V1 equals 4.9/9.8 = 0.50. Although I think it doesn't make sense to divide 9.81 by 2. At this point, I couldn't do any better.
I don't want the answer, I just want to know what should I do to solve it.

jbriggs444 said:
It's not just the template you need. You need to show your work. Tell us what things you have tried. Not just the fact that they've failed.

The work that you have shown in post #1 assumes that the initial speed is 9.81 m/s. You may not assume that. All you know is that the initial speed is v1. You also assume that the ball will have half the speed in half the height. That is simply wrong. The speed will have half its value in half the time required to reach height h, not in the time required to reach half the height. You have correctly divined that dividing by two makes no sense.

You are given two pairs of positions and speeds and you know of course that the acceleration is g down. Is there an equation among the ones that you listed that relates displacement and speed and includes the acceleration? If so, use it to express with equations what the problem is telling you that is going on.

Last edited:
Equation (v) relates the velocity to distance (height). However note that its an equation for Vy2 not Vy so do you think it likely it will be going half the speed at half the height?

The first thing to do when asked for a ratio is to set up the division. What is the numerator an denominator in the case? The find equations for each and finally see if it can be simplified. Dies anything cancel?

## 1. What is the formula for calculating the ratio in free fall motion?

The formula for calculating the ratio in free fall motion is ratio = distance/time^2. This formula is derived from the equation of motion for free fall, which is d= 0.5 * g * t^2, where d is the distance, g is the acceleration due to gravity, and t is the time.

## 2. How do you determine the value of acceleration due to gravity in free fall?

The value of acceleration due to gravity in free fall can be determined by using the formula g = 2 * d/t^2, where d is the distance and t is the time. This formula is derived from the equation of motion for free fall.

## 3. Can the ratio in free fall motion be negative?

Yes, the ratio in free fall motion can be negative. This indicates that the object is moving in the opposite direction of the acceleration due to gravity. For example, if an object is thrown upwards, the ratio will be negative during its initial ascent.

## 4. How does air resistance affect the ratio in free fall motion?

Air resistance can affect the ratio in free fall motion by slowing down the object's acceleration due to gravity. This is because air resistance creates an opposing force on the object, reducing its acceleration. However, in most cases, the effect of air resistance on the ratio is negligible and can be ignored.

## 5. Is the ratio in free fall motion affected by the mass of the object?

No, the ratio in free fall motion is not affected by the mass of the object. This is because the acceleration due to gravity is independent of the mass of the object and therefore does not affect the ratio. Both light and heavy objects will have the same ratio in free fall motion.

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