Question

a)Find the velocity of B relative to A, giving the answer in i, j form.b)Find the magnitude of the velocity of B relative to A, giving the answer to 3 significant figures.C)Find the direction of the velocity of B relative to A, giving the answer as an angle from the positive x-axis in degrees to 1 decimal place.

Answer 1

ANSWER

$\begin{gathered} (a)\text{ }(-6i+7j)ms^{-1} \\ (b)\text{ }9.22\text{ }ms^{-1} \\ (c)\text{ }130.6\degree \end{gathered}$

EXPLANATION

(a) To find the velocity of B relative to A, we have to find the vector subtraction of vectors B and A.

Hence, the velocity of B relative to A is:

$B-A=5i+3j-(11i-4j)$

Simplify the expression:

$\begin{gathered} B-A=5i-11i+3j+4j \\ B-A=(-6i+7j)ms^{-1} \end{gathered}$

That is the velocity of B relative to A.

(b) To find the magnitude of the velocity of B relative to A, apply the formula for the magnitude of a vector:

$|B|=\sqrt{x^2+y^2}$

where (x, y) represents the coordinates of the vector

Hence, the magnitude of the velocity of B relative to A is:

$\begin{gathered} |B|=\sqrt{(-6)^2+(7)^2}=\sqrt{36+49} \\ |B|=\sqrt{85} \\ |B|=9.22\text{ }ms^{-1} \end{gathered}$

(c) To find the direction of the velocity of B relative to A, apply the formula for the direction of a vector:

$\theta=\tan^{-1}(\frac{y}{x})$

Hence, the direction of the velocity of B relative to A, as an angle from the positive x-axis is:

$\begin{gathered} \theta=\tan^{-1}(\frac{7}{-6}) \\ \theta=\tan^{-1}(-1.1667) \\ \theta=130.6\degree \end{gathered}$

That is the answer.