# Curvilinear Motion: Rectangular Components

• aaronfue
In summary, the conversation discusses finding the magnitude of velocity at a specific time and verifying the correctness of a solution for a given position equation. The solution involves taking the first derivative to find the velocity and plugging in a specific time to find the magnitude of the velocity. However, there is a note that the result may not be accurate to four significant digits.
aaronfue

## Homework Statement

What is the magnitude of the velocity at t=4.00s?

I would like to see if my approach and answer is correct.

## Homework Equations

Position: r = {-30cos($\frac{\pi}{10}$t) i + 30sin($\frac{\pi}{10}$t) j - (7t) k} ft

## The Attempt at a Solution

I took the first derivative to get the velocity and my equation came out to be:

r' = {3$\pi$sin($\frac{\pi}{10}$t) i + 3$\pi$cos($\frac{\pi}{10}$t) j - (7) k} $\frac{ft}{s}$

And after plugging in t=4, my velocity vector equation was: [(8.96)i + (2.91)j - (7)k] $\frac{ft}{s}$

Then my velocity magnitude was: 11.74 $\frac{ft}{s}$

It is OK, but the result can not be accurate to four significant digits.

ehild

## 1. What is curvilinear motion?

Curvilinear motion refers to the movement of an object along a curved path.

## 2. How is curvilinear motion different from linear motion?

Curvilinear motion involves movement along a curved path, while linear motion involves movement along a straight path.

## 3. What are rectangular components in curvilinear motion?

Rectangular components in curvilinear motion refer to the horizontal and vertical components of an object's motion along a curved path.

## 4. How are rectangular components calculated in curvilinear motion?

To calculate the rectangular components of an object's motion in curvilinear motion, the horizontal and vertical components of the object's velocity and acceleration must be determined using trigonometric functions.

## 5. What are the applications of curvilinear motion in science and engineering?

Curvilinear motion is commonly used in the fields of physics, engineering, and astronomy to study the motion of objects such as planets, projectiles, and vehicles. It is also used in computer animation and video game development to create realistic movements for characters and objects.

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