Terminal Velocity: Solving for D

In summary, terminal velocity is the highest velocity that an object can reach as it falls through a fluid, occurring when the forces of gravity and air resistance are balanced. It can be calculated using the formula Vt = sqrt(2mg/pAC) and is affected by factors such as the object's mass and shape, fluid density and viscosity, and altitude or air pressure. Terminal velocity cannot be exceeded as it is the maximum speed an object can reach while falling through a fluid. It is different from free fall, which refers to the acceleration of an object towards the ground due to gravity, as terminal velocity results in a constant, maximum speed.
  • #1
student34
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Homework Statement



A man 50.0kg has a terminal velocity of 42m/s. What value of D is required to make this possible?

Homework Equations



V(terminal velocity) = (mg/D)^1/2

The Attempt at a Solution



D = (50kg*9.8m/s^2)/(42m/s)^2) = 0.28kg/m

The book's answer is 44kg/m. Is the book wrong or am I wrong?
 
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  • #2
0.28 kg/m satisfies that equation.
 
  • #3
NascentOxygen said:
0.28 kg/m satisfies that equation.

Thanks, I needed some reinforcement.
 

FAQ: Terminal Velocity: Solving for D

What is terminal velocity?

Terminal velocity is the highest velocity that an object can reach as it falls through a fluid, such as air or water. It occurs when the forces of gravity and air resistance are balanced, resulting in a constant, maximum speed.

How is terminal velocity calculated?

Terminal velocity can be calculated using the formula Vt = sqrt(2mg/pAC), where Vt is the terminal velocity, m is the mass of the falling object, g is the acceleration due to gravity, p is the density of the fluid, A is the projected area of the object, and C is the drag coefficient.

What factors affect terminal velocity?

The factors that affect terminal velocity include the mass and shape of the falling object, the density and viscosity of the fluid, and the altitude or air pressure. These variables can change the balance between the forces of gravity and air resistance, thus impacting the object's terminal velocity.

Can terminal velocity be exceeded?

No, terminal velocity is the maximum speed that an object can reach while falling through a fluid. If the forces of gravity and air resistance are balanced, the object's speed will remain constant. However, if the object changes shape or encounters a different fluid with different properties, its terminal velocity may change.

How is terminal velocity different from free fall?

Terminal velocity and free fall are two different concepts. Free fall refers to the force of gravity acting on an object, causing it to accelerate towards the ground. Terminal velocity occurs when the forces of gravity and air resistance are balanced, resulting in a constant, maximum speed. In free fall, an object will continue to accelerate until it reaches terminal velocity, at which point its speed will remain constant.

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