# Calculating Speed on a Ramp: Related Rates Problem

• fogvajarash
In summary, the conversation discusses a physics problem involving a girl entering a ramp with a given speed and height. The problem asks for the speed at which the girl comes out of the ramp, and suggests using physical concepts such as conservation of energy or calculus to solve it. The conversation also mentions the need for more information, such as the type of vehicle the girl is riding and whether she exerts any energy to get up the ramp.
fogvajarash

## Homework Statement

A girl enters a ramp with a speed of 30ft/s. The ramp has 4ft in height and 15ft in length. Calculate the speed at which she comes out of the ramp.

-

## The Attempt at a Solution

I was thinking of just using cosθ=x/z, and just plugging in the values of the derivative (when she enters the ramp) and the value of the length of the ramp and the diagonal distance (finding cosθ with tan-1θ; which gives me a final result of 8. However is this solution right? I'm not sure if my procedure is correct (and i don't have the answer to the exercise).

If the ramp is frictionless, you can use conservation of energy to figure out the change in her kinetic energy from the change in her gravitational potential energy.

$E_{total} = K + U = \text{Const}$

$\Delta E_{total} = \Delta U + \Delta K =0$

$\Delta U = mg (z_{f}-z_{i})$

$\Delta K = \frac{1}{2}m (v_{f}^{2}-v_{i}^{2})$

By knowing her initial speed and her change in height, you can figure out her final speed.

I've also used that equation, but they are asking me to use calculus and not physical concepts. That's why I'm lost.

fogvajarash said:
I've also used that equation, but they are asking me to use calculus and not physical concepts. That's why I'm lost.
You'll need to use some physical concepts, since this is a physics problem. If you want to use calculus, start with the acceleration and see if you can derive the appropriate kinematic formula.

There's a lot left out here! "A girl enters a ramp". Is the girl riding a car, a bicycle, or a horse? Or is she walking? Are we to assume that she (or her car or horse) does not exert any energy to get up the ramp?

HallsofIvy said:
There's a lot left out here! "A girl enters a ramp". Is the girl riding a car, a bicycle, or a horse? Or is she walking? Are we to assume that she (or her car or horse) does not exert any energy to get up the ramp?
She's a waterskier and enters the ramp. I'm not really sure what the problem is asking for, as it only gives out that basic information. If it's in a Calculus textbook, i really doubt i have to apply physical concepts.

## 1. What is the concept of related rates?

Related rates is a mathematical concept that deals with the changing rates of two or more related variables. It involves finding the rate of change of one variable with respect to the rate of change of another related variable.

## 2. How does the concept of related rates apply to a ramp?

In the context of a ramp, related rates can be applied to determine the rate at which an object will slide down the ramp. This involves considering the changing height and distance of the object on the ramp, as well as the angle of the ramp itself.

## 3. What are some common examples of related rates and a ramp?

Some common examples include a ball rolling down a ramp, a car driving up a hill, or water flowing out of a tank through a small hole.

## 4. How do you set up a related rates problem involving a ramp?

To set up a related rates problem involving a ramp, you must first identify the variables involved (such as height, distance, and angle) and their rates of change. Then, you can use the relationships between these variables (such as trigonometric functions) to form an equation that relates their rates of change.

## 5. What are some tips for solving related rates problems involving a ramp?

Some tips for solving related rates problems involving a ramp include drawing a diagram to visualize the problem, labeling all known and unknown quantities, and using the chain rule to differentiate the equation relating the variables. It is also important to pay attention to the units of measurement and to always check your final answer for reasonableness.

• Introductory Physics Homework Help
Replies
56
Views
1K
• Introductory Physics Homework Help
Replies
10
Views
4K
• Calculus and Beyond Homework Help
Replies
1
Views
3K
• Calculus and Beyond Homework Help
Replies
13
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
3K
• Introductory Physics Homework Help
Replies
9
Views
3K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
2K