Projectile motion with aerodynamic drag force

[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

 

[Hootenanny]

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?

 

[IceD]

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?

 

[Hootenanny]

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.

 

[rwisz]

addy

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.