Final answer:
The skaters will continue moving towards the edge of the rink with a velocity of 3.023 m/s. It will take them approximately 8.26 seconds to glide to the edge of the rink.
Step-by-step explanation:
To determine how long it will take for the skaters to glide to the edge of the rink, we need to consider their initial velocities and masses. The skater traveling north has a mass of 76 kg and a velocity of 2.3 m/s, while the skater heading west has a mass of 63 kg and a velocity of 3.9 m/s.
Since they collide and hold onto each other, their combined mass is 76 kg + 63 kg = 139 kg. To find their final velocity, we can use the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
Momentum before collision = Momentum after collision
Since the skaters hold onto each other and move together, their final velocity after the collision will be the same. Using the momentum equation:
(76 kg x 2.3 m/s) + (63 kg x 3.9 m/s) = (139 kg) x (final velocity)
Solving for the final velocity, we get:
(174.8 kg·m/s) + (245.7 kg·m/s) = (139 kg) x (final velocity)
420.5 kg·m/s = (139 kg) x (final velocity)
final velocity = 420.5 kg·m/s / 139 kg = 3.023 m/s
The skaters will continue moving with a velocity of 3.023 m/s towards the edge of the rink. To determine how long it will take them to reach the edge, we can use the formula for average velocity:
time = distance / velocity
The distance to the edge of the rink is half the diameter of the rink, so it is 50 m / 2 = 25 m. Plugging in the values:
time = 25 m / 3.023 m/s = 8.26 seconds
Therefore, it will take the skaters approximately 8.26 seconds to glide to the edge of the rink.