# Vector V1 is 8.98 units long and points along the negative x axis. Vector V2 is 4.00 units long...

## Question:

Vector V1 is 8.98 units long and points along the negative x axis. Vector V2 is 4.00 units long and points at +50.0 to the +x axis.

a) What are the x and y components of each vector?

b) Determine the sum V1 + V2.

The vector is a quantity that shows the magnitude and direction of a physical quantity.

Force is a vector.

Velocity is a vector.

Two vector quantities can be added by means of the vector algebra.

Given:

Vector V1 is 8.98 units long and points along the negative x axis. Vector V2 is 4.00 units long and points at +50.0 to the +x axis.

{eq}V_1 = - 8.98\hat i\\ V_2 = 4\cos\ 50^o \hat i + 4\ sin\ 50^o \hat j\\ {/eq}

## a):

The x component of V1 is -08.98.

The y component of the V1 is 0

The x component of V2 is 2.57.

The y component of V2 is 3.

## b):

{eq}V_1 + V_2 = - 8.98\hat i+ 4\cos\ 50^o \hat i + 4\ sin\ 50^o\hat j\\ V_1 + V_2 = -6.4\hat i + 3.06\hat j\\ {/eq}

The magnitude of the sum is, {eq}M = \sqrt{6.4^2 + 3.06^2} = 7.09 {/eq}