Question

The x component of vector is -27.3 m and the y component is +43.6 m. (a) What is the magnitude of ? (b) What is the angle between the direction of and the positive direction of x?

Answer 1

Answer:51.44 units

Step-by-step explanation:

Given

x component of vector is
`-27.3\hat{i}`

y component of vector is
`43.6\hat{j}`

so position vector is

`r=-27.3\hat{i}+43.6\hat{j}`

Magnitude of vector is

`|r|=√(27.3^2+43.6^2)`

`|r|=√(2646.25)`

|r|=51.44 units

Direction

`tan\theta =(43.6)/(-27.3)=-1.597`

vector is in 2nd quadrant thus

`180-\theta =57.94`

`\theta =122.06^(\circ)`