# Finding general solution for object falling in air

• andrey21
In summary, the conversation is about using separation of variables to solve the equation v' = (cd/M)(v^2) - g and finding the terminal velocity. The general solution is v = 20SQRT10 x ((1+Ae^(t/SQRT10))/(1-Ae^(t/SQRT10))). To find the terminal velocity, the rate of change or velocity must be set to zero.

#### andrey21

1. Using separation of variables show that:
v' = (cd/M)(v^2) - g has a general solution of:

v = 20SQRT10 x ((1+Ae^(t/SQRT10)/(1-Ae^(t/SQRT10))

## The Attempt at a Solution

Have attempted numerous times with little success help appreciated!

Divide both sides by

$$\frac{cd}{M}v^2 - g$$

Just come to the correct answer and now is asking to find the terminal velocity. How would I go about doing that?

Jamiey1988 said:
Just come to the correct answer and now is asking to find the terminal velocity. How would I go about doing that?

That would be where the rate of change or velocity is zero.

## 1. What is the general solution for an object falling in air?

The general solution for an object falling in air is the equation of motion for a falling object, which is described by the equation d = 1/2 gt^2, where d is the distance traveled, g is the acceleration due to gravity, and t is time.

## 2. How do you calculate the acceleration due to gravity?

The acceleration due to gravity can be calculated by dividing the change in velocity by the change in time. It is typically represented by the symbol g and has a constant value of 9.8 m/s^2 on Earth.

## 3. What factors affect the falling speed of an object?

The falling speed of an object is affected by several factors, including the mass and shape of the object, the air resistance or drag force acting on the object, and the acceleration due to gravity.

## 4. How does air resistance affect the motion of a falling object?

Air resistance, also known as drag force, opposes the motion of a falling object and can significantly slow down its descent. The faster the object falls, the greater the air resistance will be.

## 5. Can the general solution for an object falling in air be applied to all objects?

The general solution for an object falling in air can be applied to most objects, as long as they are falling in a vacuum or in a medium with a relatively constant density. However, for objects with a large surface area, air resistance may need to be taken into account to accurately predict the motion.