a goalie standing on a frictionless surface catches a 270.0-g puck travelling at 95.0 km/h. after catching the puck, the goalie is moving at 8.90cm/s. What is the mass of the goalie (including equipment)?
79.8 kg
To find the mass of the goalie (including equipment), we can use the principle of conservation of momentum.
Conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system.
The momentum of an object is defined as the product of its mass and velocity:
Momentum = Mass x Velocity
Before the goalie catches the puck, the momentum of the puck is given by:
Momentum of puck before = Mass of puck x Velocity of puck before
After the goalie catches the puck, the total momentum of the system (puck + goalie) is given by:
Total momentum after = (Mass of puck + Mass of goalie) x Velocity of goalie after
Since momentum is conserved, we can equate the two expressions:
Momentum of puck before = Total momentum after
Now, let's plug in the known values:
Mass of puck = 270.0 g = 0.270 kg
Velocity of puck before = 95.0 km/h = 26.38 m/s
Velocity of goalie after = 8.90 cm/s = 0.089 m/s
Equating the two expressions:
Mass of puck x Velocity of puck before = (Mass of puck + Mass of goalie) x Velocity of goalie after
0.270 kg x 26.38 m/s = (0.270 kg + Mass of goalie) x 0.089 m/s
Simplifying the equation:
7.1126 kg·m/s = (0.270 kg + Mass of goalie) x 0.089 m/s
Dividing both sides by 0.089 m/s:
Mass of goalie + 0.270 kg = 7.1126 kg
Subtracting 0.270 kg from both sides:
Mass of goalie = 7.1126 kg - 0.270 kg
Mass of goalie = 6.8426 kg
Therefore, the mass of the goalie (including equipment) is approximately 6.8426 kg.