Question

Mario, a hockey player, is skating due south at a speed of 4.79 m/s relative to the ice. A teammate passes the puck to him. The puck has a speed of 9.13 m/s and is moving in a direction of 17.8 ° west of south, relative to the ice. What are (a) the magnitude and (b) direction (relative to due south) of the puck's velocity, as observed by Mario

Answer 1

Mario's velocity vector relative to the ice is

$\vec v_{M/I}=-4.79\,\vec\jmath$

(note that all velocities mentioned here are given in m/s)

The puck is moving in a direction of 17.8 degrees west of south, or 252.2 degrees counterclockwise relative to east. Its velocity vector relative to the ice is then

$\vec v_{P/I}=9.13(\cos252.2^\circ\,\vec\imath+\sin252.2^\circ\,\vec\jmath)=-2.79\,\vec\imath-8.69\,\vec\jmath$

The velocity of the puch relative to Mario is

$\vec v_{P/M}=\vec v_{P/I}+\vec v_{I/M}=\vec v_{P/I}-\vec v_{M/I}$

$\vec v_{P/M}=-2.79\,\vec\imath-3.90\,\vec\jmath$

Then, relative to Mario,

a. the puck is traveling at a speed of $\boxed{\|\vec v_{P/M}\|=4.80}$, and

b. is moving in a direction $\theta$ such that

$\tan\theta=\dfrac{-3.90}{4.80}\implies\theta=-126^\circ$

which is about $\boxed{35.6^\circ}$ west of south.