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

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

Step-by-step 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|=√(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|=√((-6)^2+(7)^2)=√(36+49) \\ |B|=√(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)((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)((7)/(-6)) \\ \theta=\tan^(-1)(-1.1667) \\ \theta=130.6\degree \end{gathered}`

That is the answer.