Final answer:
The equation of motion for the sinking object is 19.62 N - 10 x velocity - 784.8 N = 80 kg x acceleration. At t = (60 m/s - 0 m/s) / -9.81 m/s^2, the time is -6.12 seconds, which is not achievable in this scenario.
Step-by-step explanation:
Let's analyze the forces acting on the object. The weight of the object is given by the equation: weight = mass x gravity. In this case, weight = 80 kg x 9.81 m/s^2 = 784.8 N. The buoyancy force is given by the equation: buoyancy force = (1/40) x weight of the object. So, buoyancy force = (1/40) x 784.8 N = 19.62 N. The resistive force due to water resistance is proportional to the velocity of the object, with a proportionality constant of 10 N-sec/m. Therefore, the resistive force can be written as: resistive force = 10 x velocity.
Now, let's set up the equation of motion for the object. Using Newton's second law, which states that the sum of the forces acting on an object is equal to the mass of the object times its acceleration, we can write: sum of forces = mass x acceleration. In this case, the sum of forces is the buoyancy force minus the resistive force minus the weight of the object. Therefore, the equation of motion is: 19.62 N - 10 x velocity - 784.8 N = 80 kg x acceleration.
To find the time at which the velocity of the object is 60 m/s, we can solve the equation of motion for acceleration. Rearranging the equation gives: acceleration = (19.62 N - 10 x 60 m/s - 784.8 N) / 80 kg = -9.81 m/s^2. Since gravity is pulling the object down, the acceleration is negative. Using the kinematic equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can rearrange the equation to solve for t: t = (v - u) / a = (60 m/s - 0 m/s) / -9.81 m/s^2. Evaluating the expression gives t = -6.12 seconds. However, time cannot be negative in this context, so the velocity of 60 m/s is not achievable in this scenario.