As a result of the law of conservation of momentum, the man will recoil as far as 0.034 m.
The law of conservation of momentum:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Where:
u₁ , u₂ = initial velocity of object 1 and object 2
v₁ , v₂ = final velocity of object 1 and object 2
Since both the player and the puck are initially at rest, hence u₁ = 0, u₂ = 0.
Therefore,
m₁v₁ + m₂v₂ = 0
Parameters given:
m₁ = 80 kg
m₂ = 0.150 kg
v₂ = 47 m/s
Plug the parameters into the equation,
80 . v₁ + 0.15 . 47 = 0
v₁ = - 0.088 m/s
Time the puck reach 18 m goal:
t = distance / velocity = 18 / 47 = 0.38 s
The player will recoil:
distance = velocity x t = 0.088 x 0.38 = 0.034 m = 3.4 cm
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