Final answer:
Using the terminal velocity and gravitational force, the value of 'b' in the frictional force equation was calculated to be 0.04905 kg/s. The distance before reaching 90% of the terminal velocity cannot be accurately determined with the given information, as additional details about the diamond's motion or the drag coefficient are required.
Step-by-step explanation:
Calculating 'b' in a Frictional Force Equation
To find the value of b, we know that at terminal velocity, the frictional force equals the gravitational force. This means that f = mg, where m is mass, and g is acceleration due to gravity. Given that f = -bv at terminal velocity and the mass (m) of the diamond is 10.0 g (or 0.01 kg), and assuming g is approximately 9.81 m/s², we can set mg equal to bv:
m * g = b * v
0.01 kg * 9.81 m/s² = b * 2.0 m/s
0.0981 kg*m/s² = b * 2.0 m/s
b = 0.04905 kg/s.
Finding the Distance to Reach 90% of Terminal Velocity
Using the kinematic equation v = u + at and knowing that terminal velocity is reached infinitely, we would instead use an approximate method involving the drag force equation and the fact that the acceleration is decreasing as the speed increases. However, to find an accurate distance, we would need more information, such as the coefficient of drag or additional properties of the motion, which are not given.