# Projectile motion with aerodynamic drag force

• IceD
In summary, the problem involves a projectile of mass 1300kg launched from the ground with initial velocity components of Vx=Vy=108m/s. The aerodynamic drag force is given by C(V)^2, where C=0.6. The goal is to find the range and angular momentum, both initial and final. The problem cannot be solved analytically and requires numerical analysis. The first step is to apply Newton's second law to each component of motion to obtain a system of two coupled differential equations. The question may be moved to the advanced physics section for further discussion.
IceD

## Homework Statement

A projectile of mass 1300kg is launched from the ground (x =0, y =0)
initial velocity components Vx=Vy=108m/s
aerodynamic drag force is of magnitude C(V)^2
where C = 0.6

## Homework Equations

Finding the range and angular momentum initial and final

## The Attempt at a Solution

1. I found V = 152.74 (*by V= root(Vx^2 + Vy^2)
2. and weight as 12753 kg
3. I tried to find aerodynamic drag force (FD), but I got something like 13997.70 m^2/s^2
(it should be in Newtons right?)
4. I think I'll break FD to x and y components and use them to calculate when it'll reach it's peak (Vy= 0) and based on it I'll use the the t to get the distance...but how to find it?
5. for the angle, can I assume that it was 45 degrees angle?
since Vx=Vy?
6. and I have no idea how to find the angular momentum @.@

Sorry if my working is quiet "useless" cause I'm quiet "blind" at this subject...

Thanks before :D

Regards,
IceD

This question is not a trivial one and indeed, cannot be solved analytically in terms of elementary functions. You can however, solve the system numerically.

As you say, you need to apply Newton's second law to each component (horizontal and vertical) of the motion. This will then yield a system of two coupled differential equations that you will need to sole numerically.

As I said, this problem isn't straightforward and the fact that you have posted this in the Introductory Physics forums would suggest that you are still in elementary physics classes. So I must as, are you sure that you have the question correct? How much numerical analysis have you done?

yes, I'm sure that the question is correct @.@
I found the V and the W... but can't go any further than that @.@
huff...
so should I post this question in advance physics section?

IceD said:
yes, I'm sure that the question is correct @.@
I found the V and the W... but can't go any further than that @.@
huff...
so should I post this question in advance physics section?
Have you tried to write down the two PDEs from Newton's Second law?

I think that your question is fine here, but I can move it for you if you wish.

I would suggest approaching this problem by first understanding the equations and principles involved in projectile motion with aerodynamic drag force. This includes understanding the equations for calculating the aerodynamic drag force, as well as the principles of projectile motion such as the effects of gravity and air resistance.

Based on the given information, it seems that you have correctly calculated the initial velocity and weight of the projectile. However, the calculation for the aerodynamic drag force may need to be revisited. The aerodynamic drag force is typically calculated using the equation FD = 0.5 * ρ * C * A * v^2, where ρ is the density of air, C is the drag coefficient, A is the cross-sectional area of the projectile, and v is the velocity of the projectile. Given that the density of air and cross-sectional area are not provided, it may be difficult to accurately calculate the aerodynamic drag force in this case.

In terms of finding the range and angular momentum, it would be helpful to first plot the motion of the projectile and analyze its trajectory. This can be done by breaking the initial velocity into its x and y components and using the equations for projectile motion to determine the time and distance traveled. The angle of launch can also be determined from the initial velocity components.

Finding the angular momentum will involve using the equation L = mvr, where m is the mass of the projectile, v is the velocity, and r is the distance from the axis of rotation. This can be calculated at both the initial and final points of the projectile's motion.

Overall, it is important to understand the equations and principles involved in projectile motion with aerodynamic drag force in order to accurately solve this problem. It may also be helpful to consult with a teacher or classmate for clarification and assistance.

## 1. What is projectile motion with aerodynamic drag force?

Projectile motion with aerodynamic drag force is a type of motion in which an object is projected into the air and experiences the force of air resistance, also known as aerodynamic drag. This type of motion is commonly seen in sports such as baseball, where the ball is thrown and experiences drag as it moves through the air.

## 2. What is the difference between projectile motion with and without aerodynamic drag force?

The main difference between projectile motion with and without aerodynamic drag force is the presence of air resistance. Without air resistance, an object follows a parabolic path. However, with air resistance, the object experiences a slowing force that changes its trajectory and leads to a shorter range.

## 3. How does air resistance affect the trajectory of a projectile?

Air resistance, or aerodynamic drag, affects the trajectory of a projectile by slowing down the object as it moves through the air. This leads to a shorter range and a change in the shape of the projectile's path. The amount of air resistance depends on the size, shape, and speed of the object, as well as the density of the air.

## 4. Can the effects of aerodynamic drag force be ignored in projectile motion?

No, the effects of aerodynamic drag force cannot be ignored in projectile motion. In most cases, air resistance has a significant impact on the trajectory of a projectile, especially at higher speeds. Neglecting this force can lead to inaccurate predictions and calculations.

## 5. What factors affect the amount of aerodynamic drag force experienced by a projectile?

The amount of aerodynamic drag force experienced by a projectile depends on several factors, including the size, shape, and speed of the object, as well as the density and viscosity of the air. Additionally, the orientation and surface roughness of the object can also affect the amount of drag experienced.

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