# Motion Problem: Quick Solution | 65 Chars

• metalmagik
In summary, the conversation discusses using the tradeoff between kinetic energy and potential energy to solve for the height of a cart given its initial and final velocities. The law of conservation of energy is applied by setting the change in kinetic energy equal to the change in potential energy. The final answer is .12 m, achieved by solving for the change in height using the initial and final velocities of the cart.
metalmagik
http://img128.imageshack.us/img128/5118/rampproblemec4.png

I did the first 2, I just really really need help with (e). My teacher has the answer down as .12 m...but I do not understand how to achieve height when you don't have an angle with which to achieve x velocity and y velocity. Any hints are greatly appreciated.

Last edited by a moderator:
Can you use the tradeoff between kinetic energy (related to speed) and potential energy (related to changes in height)?

GAH. you're right. Forgot about good old conservation of energy. Except, got KE and used that as PE to find h and got .012 as an answer...hmm I used .5 for velocity since that's where it ends off at...what did I do wrong?

Set $$\Delta KE = \Delta PE$$

What is the change in KE? What is the change in PE? Note how the mass term cancels out of both sides. Now solve for $$\Delta H$$

EDIT -- fixed some LaTex and my typos.

thanks for the second response :)

I did exactly that and got .012 m rather than .12 m. Here is my equation:

$1/2v^2 = gh$
$1/2(.5m/s)^2 = (-9.8m/s^2)h$

0.5m/s is not the change in velocity. The $$\Delta KE$$ is the initial KE minus the final KE.

AH I see now. I got the right answer, but why was it necessary to use $$\Delta KE$$? I guess just because we needed to find the total height above ground level at which the cart goes? I am just having trouble conceptualizing it.

Because you are using $$\Delta KE = \Delta PE$$

The total energy PE + KE is constant because of of the law of conservation of energy. The change in KE is related to the velocity in this problem. The change in PE is related to the change in height in this problem. Does that make sense?

EDIT -- clarified some wording.

It makes a little sense...Since we need the height relative to the velocity it undergoes in THAT timeframe only, we need $$\Delta KE$$?

## What is a motion problem?

A motion problem is a type of mathematical problem that involves the movement or change of an object's position over time.

## How do you solve a motion problem?

To solve a motion problem, you need to use the equation distance = speed x time. First, identify the known variables (distance, speed, or time) and plug them into the equation. Then, solve for the missing variable by rearranging the equation.

## What is the quick solution for a motion problem?

The quick solution for a motion problem is to use the formula distance = speed x time. This formula can help you quickly solve for any of the variables in a motion problem.

## What is the significance of 65 characters in a motion problem?

In a motion problem, 65 characters refer to the maximum number of characters that can be used to describe the problem. This limitation encourages problem solvers to use concise and precise descriptions.

## What are some tips for solving motion problems quickly?

Some tips for solving motion problems quickly include identifying the known variables, using the formula distance = speed x time, converting units if necessary, and checking your answer for reasonableness.

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