One swimmer in a relay race has a 0.580 s lead and is swimming at a constant speed of 3.98 m/s. he has 51.3 m to swim before reaching the end of the pool. a second swimmer moves in the same direction as the leader. what constant speed must the second swimmer have in order to catch up to the leader at the end of the pool?

4.17 m/s

Explanation:

The equation for distance for a constant velocity is given by:

x = v * t, x = distance, v = velocity, t = time

1. The time for the first swimmer to reach the end of the pool:

t₁ = x/v₁ = 51.3m / 3.98m/s

2. The second swimmer will be at the same location at a time t₂, from where she has 0.58s less to reach the end of the pool than the first swimmer. The velocity for the second swimmer will be:

v₂ = x/t₂ = 51.3 / (t₁ - 0.58s) = 51.3m / (51.3m / 3.98m/s - 0.58s)