Jack and Jill are skating. Jill has a mass of 50 kg, Jack has a mass of 80 kg. At t=0 seconds Jill starts skating across a 50 m diameter rink at a speed of 3 m/s. After 3 seconds Jack skates after her with a speed of 5 m/s. When they meet, Jack scoops up Jill and they glide to the other end of the rink together. At what time t in seconds do they reach the other side of the rink? You can neglect any friction of the ice or drag.

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To determine the time at which Jack and Jill reach the other side of the rink, we first need to find out the distance Jill travels before Jack catches up with her.

Jill's distance = Jill's speed * time
Jill's distance = 3 m/s * 3 s = 9 m

Now, we know the distance Jill covers before Jack catches up is 9 meters. From that point onwards, Jack and Jill are together and will travel the remaining distance of the rink.

Remaining distance of the rink = Total rink distance - Jill's distance
Remaining distance = 50 m - 9 m = 41 m

To determine the time it takes for Jack and Jill to cover the remaining distance together, we need to calculate their combined speed.

Combined speed = (Jack's mass * Jack's speed + Jill's mass * Jill's speed) / (Jack's mass + Jill's mass)
Combined speed = (80 kg * 5 m/s + 50 kg * 3 m/s) / (80 kg + 50 kg)
Combined speed = (400 kg·m/s + 150 kg·m/s) / 130 kg
Combined speed = 550 kg·m/s / 130 kg
Combined speed ≈ 4.23 m/s

Now, we can determine the time it takes for Jack and Jill to reach the other side of the rink.

Time = Distance / Speed
Time = 41 m / 4.23 m/s
Time ≈ 9.69 s

Therefore, Jack and Jill will reach the other side of the rink approximately after 9.69 seconds.