In: Physics
Mario, a hockey player, is skating due south at a speed of 6.35 m/s relative to the ice. A teammate passes the puck to him. The puck has a speed of 8.09 m/s and is moving in a direction of 22.0 ° 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?
a)
Consider east-west direction along x-axis and north-south direction along y-axis
= velocity of mario relative to ice = 0 i - 6.35 j
= velocity of puck relative to ice = - (8.09 Cos22) i - (8.09 Sin22) j = - 7.5 i - 3.03 j
= velocity of puck relative to mario
velocity of puck relative to mario is given as
= -
= (- 7.5 i - 3.03 j) - (0 i - 6.35 j)
= - 7.5 i + 3.3 j
magnitude is given as
|| = Sqrt((- 7.5)2 + (3.3)2)
|| = 8.2 m/s
b)
Direction is given as
= 90 + tan-1 (3.3/7.5)
= 113.75 deg