Question

The x-component is 8 m/s east; the y-component is 14.5 m/s North. (a) What is the value of the resultant vector? (b) What is the angle of the resultant vector?

Answer 1

Step-by-step explanation:

Given that,

The x-component is 8 m/s east and y-component is 14.5 m/s North.

(a) As both x and y components are perpendicular to each other. Their resultant is given by :

`R=√(x^2+y^2) \\\\R=√((8)^2+(14.5)^2) \\\\R=16.56\ m/s`

(b) Let
`\theta` is the resultant vector. So,

`\tan\theta=(y)/(x)\\\\\theta=\tan^(-1)((y)/(x))\\\\\theta=\tan^(-1)((14.5)/(8))\\\\\theta=61.11^(\circ)`

Hence, the resultant is 16.56 m/s and the angle of the resultant vector is 61.11 degrees.