Final answer:
The mass of the male diver is 78.1 kg.
Step-by-step explanation:
In simple harmonic motion, the period is defined as the time taken for one complete cycle of the motion. The period is inversely proportional to the square root of the mass of the object. Mathematically, we can express this relationship as:
T = 2π√(m/k),
where T is the period, m is the mass, and k is the spring constant.
In this case, the period of the first diver is 0.800 s, and the mass is 55.0 kg. The period of the second diver is 1.05 s. Since we are given that the mass of the board is negligible, we can assume that the spring constants for both divers are the same. So, we can set up an equation using the formula for the period:
0.800 = 2π√(55/k).
Similarly, for the second diver:
1.05 = 2π√(m/k).
By comparing the two equations, we can see that the periods are only different due to the different masses. Therefore, if we solve for m in terms of k in one equation and substitute it into the other equation, we can find the mass of the second diver. Solving for k using the first equation gives us:
k = (4π2) / (0.82).
Substituting this into the second equation gives us:
1.05 = 2π√(m / ((4π2) / (0.82))).
Simplifying, we find that m = 78.1 kg.
Therefore, the correct answer is d) (78.1 kg).