10. a boy on board a cruise ship drops a 30.0 gm marble into the ocean. if the resistive force proportionality constant is 0.500 kg/s, what is the terminal speed of the marble in m/s?

General
1
  1. a boy on board a cruise ship drops a 30.0 gm marble into the ocean. if the resistive force proportionality constant is 0.500 kg/s, what is the terminal speed of the marble in m/s?
2

What is the terminal speed of the marble in m/s?

Answer:
To calculate the terminal speed of the marble, we first need to determine the net force acting on the marble. The net force is given by the formula:

F_{net} = mg - kv

Where:

  • m = 0.0300 kg (mass of the marble)
  • g = 9.8 m/s^2 (acceleration due to gravity)
  • k = 0.500 kg/s (resistive force proportionality constant)
  • v (terminal speed of the marble)

At terminal speed, the net force is equal to zero:

0 = mg - kv

Substitute the values into the equation:

0 = (0.0300 kg)(9.8 m/s^2) - (0.500 kg/s)v

0 = 0.294 N - (0.500 kg/s)v

Now, solve for v :

(0.500 kg/s)v = 0.294 N

v = \frac{0.294 N}{0.500 kg/s}

v = 0.588 m/s

Therefore, the terminal speed of the marble is 0.588 m/s .