Question

Question #97fb1

Answer 1

`49.810hati +4.358hatj`

Explanation:

We're asked to find the components of a vector, given its magnitude and direction.

Vectors are a fundamental concept in linear algebra and physics, so it would be useful to remember some relatively simple equations to calculate the components of them.

For magnitude `||vecv||` and direction `theta`, the components of the vector are given by

• `ul(x = ||vecv||costheta`

• `ul(y = ||vecv||sintheta`

(You may recognize these for calculating the corresponding rectangular coordinate of a polar one, where we use the equations `x = rcostheta` abd `y = rsintheta`.)

Thus, we have

`x = 50cos(5^"o") = 49.810`

`y = 50sin(5^"o") = 4.358`

Or, in unit vector component notation,

`color(red)(ulbar(|stackrel(" ")(" "49.810hati +4.358hatj" ")|)`

`hati` corresponds to the `x`-component (horizontal), and `hatj` corresponds to the `y`-component (vertical).