# 03.1

## Contents

## Problem One

Find the components of this vector:

**To solve this problem you use:**

To solve:

## Problem Two

Find the components of this vector:

Again:

So, we do the same thing as before. This time, **don't forget that must always be a trig angle!**

## Problem Three

Convert this vector component vector to an angle magnitude vector. Draw it as an arrow, and label any angle it makes with its value, and find the magnitude.

C = 13.2 m/s x + 5.70 m/s y

We solve this problem like the first two, only in reverse. The first thing that you do is draw out the equation without lifting your pen. It should look like this:

Using SOHCAHTOA, we can take the inverse tangent (the arctan) of these values to find the angle, and using the pythagorean theorem we can take the square root of x squared plus y squared to get the magnitude.

**Mag = 14.4 m/s**

**Angle = 23.4 ^{o}**

**Angle Magnitude: 14.4 m/s @ 23.4**

^{o}## Problem Four

Given:

Find:

D+E=_________x + _________y

E-D=_________x + _________y

To solve this problem, you add and subtract the vector components like basic arithmetic.

### Finding D+E

With this problem, you simply add the corresponding values.

+___________________________

### Finding E-D

As with the previous problem, you subtract the D values from the E values to find the answer.

-___________________________

## Problem Five

Calculate the sum of vectors A and B (From problem 1 and 2). Draw the resultant vector as an angle magnitude vector. (Label your angle and magnitude clearly – use an arrow) Do your work on the back of this sheet, and label and describe the three steps for doing so.

### Sum of vectors

Calculate the sum of the two vectors

+___________________________

### Draw the vector

Label the angle, sides, and vector.

### Calculate the Angle Magnitude

Do the inverse tangent and square root of the two distances squared. Write these values as angle magnitude.

**Mag = 36.8 m/s**

**Angle = 6.97 ^{o}**

**Angle Magnitude: 36.8 m/s @ 6.97**

^{o}