9 An ice hockey puck of mass 170 g enters the goal with a momentum of ⟨0, 0, −6.3⟩ kg m/s, crossing the goal line at location ⟨0, 0,−26⟩ 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 xz plane.)

The given data can be listed below,

• The mass of the ice hockey is $m=170g\left(\frac{1kg}{1000g}\right)=0.170kg$,
• The momentum of the ice hockey puck is ,
• The initial location of the puck is, .
• The elapsed time of puck is, $∆t=0.4s$.

One of the most significant characteristics characterising motion is the object's momentum, which is defined as the mass times velocity of the object.

The velocity of the hockey puck is given by,

$\stackrel{\rightharpoonup }{v}=\frac{\stackrel{\rightharpoonup }{p}}{m}$

Here,$\stackrel{\rightharpoonup }{p}$ is the momentum of the hockey puck and m is the mass of the hockey puck.

Substitute all the values in the above,

The velocity of the puck can also be expressed as,

$\stackrel{\rightharpoonup }{r}=\frac{\stackrel{\rightharpoonup }{r_f}-\stackrel{\rightharpoonup }{r_i}}{∆t}$

Here, $\stackrel{\rightharpoonup }{r}$is the final location of the hockey puck, $\stackrel{\rightharpoonup }{r}$is the initial location of the hockey puck and $∆t$is the time elapsed.

Rearrange above expression for initial location.

$\stackrel{\rightharpoonup }{r_f}=\stackrel{\rightharpoonup }{r_i}-\stackrel{\rightharpoonup }{v}∆t$

Substitute all the values in the above expression.

Thus, the location of the puck when it was hit by the player is .