# How Long Does It Take a Raindrop to Reach 63% of Its Terminal Velocity?

• peweee17
In summary, terminal velocity time is the time it takes for an object to reach its maximum falling speed. It is affected by factors such as weight, shape, air density, and surface area of the object. The formula for calculating terminal velocity time is t = (2m/gCd)^1/2, but this assumes the object is falling in a vacuum. It can be changed by altering these factors or changing the medium through which the object is falling. Understanding terminal velocity time is important in fields such as physics and engineering for designing and predicting the behavior of objects in motion.
peweee17

## Homework Statement

The terminal velocity of a 2×10−5 kg raindrop is about 7m/s. Assuming a drag force Fd= - bv,
Assuming a drag force determine the time required for such a drop, starting from rest, to reach 63% of terminal velocity.

Fd=-bv
Sum of F-ma

## The Attempt at a Solution

I use Fd=-bv to solve for b then used Fd-Fg=ma and reduced that to dv/dt=-g-(bv/m) but don't know how to determine time.

Last edited:
You need to show some work before we can help you: what have you tried?

To determine the time required for the raindrop to reach 63% of its terminal velocity, we can use the equation for velocity with respect to time under constant acceleration:

v = v0 + at

Where v is the final velocity (in this case, 63% of the terminal velocity), v0 is the initial velocity (which is 0 since the raindrop starts from rest), a is the acceleration (which is the acceleration due to gravity, -9.8 m/s^2), and t is the time we are trying to find.

We can rewrite the equation to solve for t:

t = (v - v0)/a

Substituting in the values given in the problem, we get:

t = (0.63 * 7 m/s - 0 m/s)/(-9.8 m/s^2) = 0.045 seconds

Therefore, it would take approximately 0.045 seconds for the raindrop to reach 63% of its terminal velocity.

## What is terminal velocity time?

Terminal velocity time is the amount of time it takes for an object to reach its maximum falling speed, also known as terminal velocity. This occurs when the drag force acting on the object is equal to the force of gravity pulling it down.

## What factors affect terminal velocity time?

The factors that affect terminal velocity time include the weight and shape of the object, the air density, and the surface area of the object. Objects with greater surface area or lighter weight will have a longer terminal velocity time, while objects with smaller surface area or heavier weight will have a shorter terminal velocity time.

## How is terminal velocity time calculated?

The formula for calculating terminal velocity time is t = (2m/gCd)^1/2, where t is the time, m is the mass of the falling object, g is the acceleration due to gravity, and Cd is the drag coefficient of the object. This formula assumes that the object is falling in a vacuum. In reality, the calculation is more complex and takes into account air resistance.

## Can terminal velocity time be changed?

Yes, terminal velocity time can be changed by altering the factors that affect it. For example, increasing the weight or surface area of the object will result in a longer terminal velocity time. Additionally, changing the medium through which the object is falling, such as from air to water, can also affect terminal velocity time.

## Why is terminal velocity time important?

Terminal velocity time is important because it helps us understand how objects fall and how different factors can affect their speed. It is also important in fields such as physics and engineering, where knowledge of terminal velocity time is necessary for designing and predicting the behavior of objects in motion.

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