# Resolve Kinematics Problem: x, h, g

• FlukeATX
In summary, the problem involves a ball rolling horizontally off a tabletop and striking the floor a distance x away. The questions ask for the time the ball is in the air and its speed at the instant it leaves the table, in terms of given variables and g. The solution involves finding the time using the height and then finding the horizontal velocity using the distance and time.
FlukeATX
[Resolved] Kinematics problem?

## Homework Statement

A small ball rolls horizontally off the edge of a tabletop of height h. It strikes the floor a distance x horizontally away from the edge of the table. (a) How long is the ball in the air? (b) What is its speed at the instant it leaves the table? Please give your answer in terms of the given variables and g.

## Homework Equations

I'm not sure, since there's no numbers involved and it just wants symbolic answers. I'd think it'd be one of the standard kinematics formulas, but there's only two knowns, acceleration and displacement.

## The Attempt at a Solution

I have no idea where to start. There is no initial velocity given, no final velocity given, and no time given (in fact, that's what the question is looking for). So, how can this problem be solved if there are only two knowns? It's not the fact that they're looking for the answers in terms of x,h,g that's bothering me, I'm not sure how to approach this even if there was actual values.

Any help is appreciated!

Last edited:
Welcome to PF.

What they want you to do is express the distance, which is the horizontal velocity times the time for it to fall to the floor.

The time you can figure from the height.

But the problem is that I do not know the horizontal velocity. I suppose this could be found by dividing the distance by the time, but I am not sure how to find the time. You say it can be found by the height, but how? Am I on the right track here:

Vy = 0
d = h
a = g = -9.8
t = ?

d=Vyt + 1/2gt^2
d=1/2gt^2
2d=gt^2
2d/g=t^2
t=sqrt(2d/g)

Does that make sense?

Then I could find the horizontal velocity by:
Vx=d/t
Vx=d/(sqrt(2d/g))Sound right?

Just submitted it through the wileyplus system and the above is correct. Thanks for the help, got the wheels turning!

Last edited:
FlukeATX said:
Thanks for the help, got the wheels turning!

That of course is the idea.

Congrats and good luck.

## What is the formula for solving kinematics problems?

The formula for solving kinematics problems involving displacement (x), initial height (h), and gravitational acceleration (g) is:
x = h + 1/2*g*t^2

## How do I determine the value of gravitational acceleration (g) in a kinematics problem?

The value of gravitational acceleration (g) on Earth is commonly accepted as 9.8 m/s^2. However, this value may vary slightly depending on location and elevation.

## How do I solve for time (t) in a kinematics problem?

To solve for time (t) in a kinematics problem, use the formula:
t = sqrt(2*x/g)

## What units should be used for displacement (x) and height (h) in kinematics problems?

Displacement (x) and height (h) should be measured in meters (m) for consistency with the formula for solving kinematics problems.

## What are some common misconceptions about solving kinematics problems?

Some common misconceptions about solving kinematics problems include neglecting to consider acceleration due to gravity (g), using incorrect units, and not accounting for the initial height (h) in the displacement formula.

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