A 0.105-kg hockey puck moving at 30 m/s is caught and held by a 80-kg goalie at rest. With what speed does the goalie slide on the ice?
Well, to calculate the goalie's speed after catching the puck, we can use the law of conservation of momentum. The initial momentum of the hockey puck is equal to the final momentum of the goalie and the puck combined. Since momentum is defined as mass times velocity, we have:
Initial momentum of the puck = Final momentum of the goalie and the puck
(0.105 kg) * (30 m/s) = (0.105 kg + 80 kg) * v
Now we can solve for v, which is the goalie's speed after catching the puck:
v = (0.105 kg * 30 m/s) / (0.105 kg + 80 kg)
v ≈ 0.0762 m/s
So, the goalie will slide on the ice with a speed of approximately 0.0762 m/s. Well, that's not a very impressive shot, but hey, at least the goalie caught it!
To find the speed at which the goalie slides on the ice, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum before the collision can be calculated by multiplying the mass of the puck (0.105 kg) by its velocity (30 m/s). The momentum after the collision is the product of the combined mass of the goalie and the puck (80 kg + 0.105 kg) and the final velocity.
Using the equation for conservation of momentum:
(mass of puck)(initial velocity of puck) + (mass of goalie)(initial velocity of goalie) = (mass of goalie + mass of puck)(final velocity)
(0.105 kg)(30 m/s) + (80 kg)(0 m/s) = (80 kg + 0.105 kg)(final velocity)
3.15 kg · m/s = 80.105 kg · m/s
Now, we can solve for the final velocity by dividing both sides of the equation by the total mass of the goalie and the puck.
final velocity = 3.15 kg · m/s / 80.105 kg
final velocity ≈ 0.039 m/s
Therefore, the goalie slides on the ice with a speed of approximately 0.039 m/s.
To find out the speed at which the goalie slides on the ice, we can use the law of conservation of momentum. According to this law, the total momentum before the catch is equal to the total momentum after the catch.
Let's denote the speed of the goalie after the catch as v_g and the velocity of the puck before the catch as v_puck.
The momentum of the puck before the catch is given by:
momentum_puck = mass_puck * velocity_puck
Substituting the given values:
momentum_puck = 0.105 kg * 30 m/s
The momentum of the goalie and puck together after the catch is given by:
momentum_after_catch = (mass_puck + mass_goalie) * v_g
Substituting the given values:
momentum_after_catch = (0.105 kg + 80 kg) * v_g
Since momentum is conserved, we can set up the equation:
momentum_puck = momentum_after_catch
0.105 kg * 30 m/s = (0.105 kg + 80 kg) * v_g
Now we can solve for v_g:
0.105 kg * 30 m/s = 80.105 kg * v_g
Dividing both sides by 80.105 kg:
v_g = (0.105 kg * 30 m/s) / 80.105 kg
Calculating the above expression, we find:
v_g ≈ 0.039 m/s
Therefore, the goalie slides on the ice with a speed of approximately 0.039 m/s.