Particle A has velocity (8i - 3j)ms^-1 and particle B has velocity (15i - 8j)ms^-1.
A) Find the speed of B
B)Find the velocity of B relative to A
A) Speed is just the magnitude of the velocity vector:
So, if particle B has velocity (15i - 8j) $\displaystyle ms^{-1}$, the speed is:
$\displaystyle v = \sqrt{15^2 - 8^2}$
$\displaystyle v = \sqrt{225 - 64}$
$\displaystyle v = \sqrt{161}$
$\displaystyle v = 12.7 ms^{-1}$
B) Relative velocity is just the difference of the velocities, so the velocity of B relative to A is:
$\displaystyle (15i - 8j) - (8i - 3j) = (7i - 5j) ms^{-1}$