You are given three displacement vectors: with magnitude 5.0 m in the direction of 60o below the negative x-axis, vector, has an x-component of +2.5 m and a y-component of +6.0 m and vector has magnitude of 2.5 m in the negative y-axis.
Find the vector so that .
Calculate the magnitude of vector .
See previous post.
To find the vector so that , we need to add up the three given displacement vectors: , , and .
To calculate the x-component of vector , we add up the x-components of the individual vectors:
= x-component of + x-component of + x-component of
= +2.5 m + 0 + 0
= 2.5 m
To calculate the y-component of vector , we add up the y-components of the individual vectors:
= y-component of + y-component of + y-component of
= 0 + +6.0 m + (-2.5 m)
= +3.5 m
Therefore, the vector so that is = (2.5 m, 3.5 m).
To calculate the magnitude of vector , we can use the Pythagorean theorem:
Magnitude of = √( x-component of ^2 + y-component of ^2)
= √((2.5 m)^2 + (3.5 m)^2)
= √(6.25 m^2 + 12.25 m^2)
= √(18.5 m^2)
= 4.30 m (rounded to two decimal places)
Therefore, the magnitude of vector is 4.30 m.