Question #97fb1

1 Answer
Nathan L.
Aug 19, 2017

#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).

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