Question

An ice hockey puck of mass 170 g enters the goal with a momentum of < 0,0, -6.6 > kg·m/s, crossing the goal line at location < 0,0, -29 > m relative to an origin in the center of the rink. The puck had been hit by a player 0.4 s before reaching the goal. What was the location of the puck when it was hit by the player, assuming negligible friction between the puck and the ice? (Note that the ice surface lies in the x⁢z plane. Express your answer in vector form.)

Answer 1

Answer:

$<0, 0, -44.528>\ m$

Explanation:

p = Momentum = <0, 0, -6.6> kgm/s

m = Mass of puck = 170 g

Velocity is given by

$v=\dfrac{p}{m}\\\Rightarrow v=\dfrac{<0, 0, -6.6>}{0.17}\\\Rightarrow v=<0, 0, 38.82>\ m/s$

The position is given by

$r_i=r_f-v\Delta t\\\Rightarrow r_i=<0, 0, -29>-<0, 0, 38.82>0.4\\\Rightarrow r_i=<0, 0, -44.528>\ m$

The location is $<0, 0, -44.528>\ m$

Answer 2

The location of the puck when it is hit by the player is 13.47 in -ve z- direction.

An impulse is provided to the puck when it is hit, and the ball gets momentum.

Now momentum is given by:

p = mv

where, p = momentum = (0,0,-6.6)kgm/s, the puck is moving only in the z-direction.

            m =  mass of the puck = 170g = 0.17 kg

            v = velocity of the puck

v = p/m

v = (0,0,-6.6)/0.17

v = (0,0,-38.82) m/s

Now to calculate the location when it was hit 4s earlier:

$r_0=r-vt\\r_0=(0,0,-29) - (-38.82)*0.4\\r_0=(0,0,-13.47)$

The location of the puck was 13.47 in -ve z-direction

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