# What is the position of a falling ball given drag force and unknown velocity?

• hello337
In summary, the conversation discusses a problem with calculating the velocity of a ball falling, due to uncertainty about the meaning of v in the equation for drag force. The drag force is defined as -C * ||v(t)|| * v, where C is a constant, v(t) is the velocity, and v is either v(t) or v(t)/|v(t)|. The conversation suggests that v is likely a unit vector in the direction of the velocity.
hello337

## Homework Statement

I have to make a plot. This plot must illustrates a position of a ball, which is falling. My problem is that I don't know what v is in this equation.
drag force= -C * ||v(t)|| * v

## Homework Equations

To calculate the velocity:
v(t+dt)=v(t)+a(t)*dt
where t is time and dt is Δt

The position:
x(t+dt)=x(t)+v(t)*dt

To find a(t) (the acceleration) I use:
a(t)=F(t)/M

where M is the mass f the ball and F(t):

F(t)=force from gravity + drag force

And drag force is:
drag force= -C * ||v(t)|| * v

## The Attempt at a Solution

I have discussed it with some from my class and some say v is v(t-dt) .. other say it is just v(t).

hello337 said:

## Homework Statement

I have to make a plot. This plot must illustrates a position of a ball, which is falling. My problem is that I don't know what v is in this equation.
drag force= -C * ||v(t)|| * v

Welcome to Physics Forums.

That looks like it might be a unit vector in the direction of the velocity. I notice that there's a "-" in front of the constant C. That would make the drag force operate in the opposite direction to the velocity, which is expected.

Thank you! So you think that v is v(t) ? :)

More likely v = v(t)/|v(t)| , making it a unit vector (magnitude of unity).

I would say that the velocity, v, in this equation is most likely referring to the instantaneous velocity of the ball at a specific time, t. This velocity would change as the ball falls due to the effects of drag force and gravity. Therefore, to accurately plot the position of the ball, you would need to calculate the velocity at each time step, using the equations provided, and then use that velocity to calculate the position of the ball. This would result in a continuous plot of the ball's position as it falls.

In terms of the discrepancy among your classmates, it is possible that some are referring to the velocity at the beginning of the time step (v(t)) and others are referring to the velocity at the end of the time step (v(t+dt)). In either case, both values would be needed to accurately calculate the position of the ball. It is important to clarify this point with your teacher or classmates to ensure everyone is on the same page and using the same definitions in their calculations.

## 1. What is drag and how does it affect the position of a ball?

Drag is a force that acts on an object as it moves through a fluid, such as air or water. It is caused by the resistance of the fluid against the motion of the object. In the case of a ball, drag acts in the opposite direction of its motion and can cause the ball to slow down or change direction.

## 2. What factors affect the amount of drag on a ball?

The amount of drag on a ball can be influenced by several factors, including the speed of the ball, the density of the fluid it is moving through, the shape and surface area of the ball, and the viscosity of the fluid. These factors can determine the magnitude and direction of the drag force on the ball.

## 3. How does the position of a ball affect the amount of drag it experiences?

The position of a ball can affect the amount of drag it experiences by changing the direction and magnitude of the drag force. For example, a ball moving with its front facing the direction of motion will experience less drag compared to a ball moving with its side facing the direction of motion.

## 4. Can the position of a ball be used to minimize drag?

Yes, the position of a ball can be strategically adjusted to minimize drag. For instance, a spherical ball will experience less drag when it is moving with its front facing the direction of motion, so athletes may adjust their body position to reduce drag and increase speed.

## 5. How is drag related to the trajectory of a ball?

The drag force acting on a ball can influence its trajectory by causing it to slow down or change direction. This is particularly important in sports such as golf or tennis, where players need to consider the amount of drag on the ball in order to accurately predict its trajectory and aim their shots.

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