Question

Look at the following picture. What would be the resultant vector of A+B? vector b is 4.78m 67 degress vector a 21 degrees 11.3m

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Answer 1

The resultant vector, A+B, has a Magnitude of 15.02 meters and an angle of 34.23 degrees

Explanation:

We need to convert the vectors given to x,y coordinate form.

We use the formula below:

`x=ACos\theta`

`y=ASin\theta`

Where A is the magnitude and
`\theta` is the angle.

Vector A:

`x=ACos\theta\\x=(11.3)Cos(21)\\x=10.55`

and

`y=(11.3)Sin(21)\\y=4.05`

Vector B:

`x=(4.78)Cos(67)\\x=1.87`

and

`y=(4.78)Sin(67)\\y=4.40`

Now we can write the vectors as:

A = <10.55,4.05>

B = <1.87,4.40>

To add, A+B, we have:

A + B = <10.55+1.87, 4.05+4.40>

A + B = < 12.42, 8.45 >

To convert this into magnitude/degree format:

Magnitude =
`√((12.42)^2 + (8.45)^2) =15.02`

Angle =
`Tan^(-1)((8.45)/(12.42))=34.23`