At the centre of a circular ice rink, a 89.0 kg ice skater moving 1.80 m/s north hits and grabs onto a 59.0 kg ice skater who had been traveling west at 5.35 m/s. If the skaters hold onto each other and the rink has a 36.0 m diameter, what is the amount of time for the skaters to reach the edge of the rink?

To solve this problem, we need to use the principles of conservation of momentum and kinematics.

Step 1: Conservation of Momentum The total momentum before the collision is equal to the total momentum after the collision.

The momentum of the first skater (P1) before the collision is mass1 * velocity1 = 89.0 kg * 1.80 m/s = 160.2 kg*m/s north.

The momentum of the second skater (P2) before the collision is mass2 * velocity2 = 59.0 kg * 5.35 m/s = 315.65 kg*m/s west.

Since these two momenta are at right angles to each other, we can find the resultant momentum (P) using Pythagoras' theorem: P = sqrt(P1^2 + P2^2) = sqrt((160.2 kgm/s)^2 + (315.65 kgm/s)^2) = 350.8 kg*m/s.

Step 2: Find the velocity of the skaters after the collision The total mass of the skaters after the collision is mass1 + mass2 = 89.0 kg + 59.0 kg = 148.0 kg.

The velocity (v) of the skaters after the collision is the total momentum divided by the total mass: v = P / (mass1 + mass2) = 350.8 kg*m/s / 148.0 kg = 2.37 m/s.

Step 3: Find the time to reach the edge of the rink The radius of the rink is half the diameter, so the distance (d) to the edge of the rink is 36.0 m / 2 = 18.0 m.

The time (t) it takes to reach the edge of the rink is the distance divided by the velocity: t = d / v = 18.0 m / 2.37 m/s = 7.59 s.

So, it takes approximately 7.59 seconds for the skaters to reach the edge of the rink.

To solve this problem, we need to use the principles of conservation of momentum and kinematics.

Step 1: Conservation of Momentum The total momentum before the collision is equal to the total momentum after the collision.

The momentum of the first skater (P1) before the collision is mass1 * velocity1 = 89.0 kg * 1.80 m/s = 160.2 kg*m/s north.

The momentum of the second skater (P2) before the collision is mass2 * velocity2 = 59.0 kg * 5.35 m/s = 315.65 kg*m/s west.

Since these two momenta are at right angles to each other, we can find the resultant momentum (P) using Pythagoras' theorem: P = sqrt(P1^2 + P2^2) = sqrt((160.2 kgm/s)^2 + (315.65 kgm/s)^2) = 350.5 kg*m/s.

Step 2: Find the Velocity After Collision The total mass after the collision is mass1 + mass2 = 89.0 kg + 59.0 kg = 148.0 kg.

The velocity (v) of the skaters after the collision is the total momentum divided by the total mass: v = P / (mass1 + mass2) = 350.5 kg*m/s / 148.0 kg = 2.37 m/s.

Step 3: Find the Time to Reach the Edge of the Rink The radius of the rink is half the diameter, so it's 36.0 m / 2 = 18.0 m.

The time (t) it takes for the skaters to reach the edge of the rink is the distance to the edge divided by their velocity: t = distance / velocity = 18.0 m / 2.37 m/s = 7.59 s.

So, it will take approximately 7.59 seconds for the skaters to reach the edge of the rink.