How come "terminal velocity" and "final velocity" are different?

In summary, the conversation discusses the velocity of a bullet shot perpendicular to the ground with air resistance. The equations for upward and downward velocity are given, and it is noted that terminal velocity is the maximum velocity due to air resistance. The final velocity of the bullet is shown to be smaller than terminal velocity, which may be due to hitting the ground before reaching terminal velocity. The concept of terminal velocity and its relationship to final velocity is also mentioned.
  • #1
Ted goldmund lee
3
0

Homework Statement



Someone shot the bullet perpendicular to the ground. And there is air resistance.
Velocity of bullet is
v^2 = Ae^(-2kx)-g/k upward
v^2 = g/k-Be^(2kx) downward

A,B is constant, g is a gravitational acceleration, k = c2/m , c2 is a resistance constant, m is a mass of bullet.

When air resistance is C2v^2 show that final speed of the bullet is

VoVt/Root(Vo^2+Vt^2) , Vo is initial velocity and Vt is terminal velocity.

Homework Equations



I thought that terminal velocity is the velocity when there is no net force on the object.
Since there is no parasutre, shouldn't the final velocity is same with terminal velocity?
How come final velocity is smaller than terminal velocity...
( I am pretty sure in this question we don't have to consider air density )

The Attempt at a Solution



upload_2019-2-27_23-46-25.png

I did solve this mathmetically but I just don't understand the physical concept.
How can something be slower when net force on it is zero.
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  • #2
Ted goldmund lee said:
Since there is no parasutre, shouldn't the final velocity is same with terminal velocity?
Terminal velocity is the fastest it can go due to air resistance. Final velocity may be less if it hits the ground before making it all the way up to terminal velocity.
 
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Related to How come "terminal velocity" and "final velocity" are different?

1. What is terminal velocity?

Terminal velocity is the maximum constant speed that an object can reach when falling through a fluid, such as air or water. It is achieved when the upward force of air resistance is equal to the downward force of gravity on the object.

2. What is final velocity?

Final velocity is the speed at which an object ends its motion. It can be influenced by various factors such as acceleration, air resistance, and friction.

3. Why are terminal velocity and final velocity different?

Terminal velocity and final velocity are different because they are measuring different stages of an object's motion. Terminal velocity is the maximum speed that an object can reach while falling, while final velocity is the speed at which the object comes to a complete stop.

4. How is terminal velocity calculated?

Terminal velocity can be calculated by using the formula: Vt = √(2mg/pAC), where Vt is the terminal velocity, m is the mass of the 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.

5. Can an object's final velocity be greater than its terminal velocity?

No, an object's final velocity cannot be greater than its terminal velocity. This is because once an object reaches its terminal velocity, the forces acting on it are balanced and it can no longer accelerate. Therefore, its final velocity will be equal to its terminal velocity.

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