Solving the Projectile Motion Problem With Air Drag

In summary, the problem involves a projectile with mass m being fired upward with an initial speed v0. The air drag is given by F(v)=-kmv2, and it is required to show that the projectile reaches a height of h=1/2k*ln[1+(kv0^2/g)]. The approach involves using the equation F0+F(v) = mv(dv/dx) and solving for the differential equation. However, the person asking for help was not able to solve it, as they have not taken differential equations yet. They proposed the equation ma=-mg-c1v, but it is unclear what "c1v" represents.
  • #1
Varnson
23
0

Homework Statement


A projectile with mass m is fired upward with an initial speed v0. If the air drag varies with the square of speed F(v)=-kmv2 show that the projectile reaches a height of
h=1/2k*ln[1+(kv0^2/g)]



Homework Equations


F0+F(v) = mv(dv/dx)


The Attempt at a Solution


I am a little confused on how to get started and tackle this problem! Any pointers? Thanks for the help!
 
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  • #2
Were you able to get the differential equation?
 
  • #3
I was not able to get the diff. eq. I have not had any diff. eq. classes yet, so I am teaching myself as I go along in my mechanics course. Would it be ma=-mg-c1v?
 
  • #4
What is "c1v"?
 

1. How does air drag affect the trajectory of a projectile?

Air drag, also known as air resistance, is a force that acts on a projectile as it travels through the air. This force acts in the opposite direction of the projectile's motion and it increases as the projectile's velocity increases. As a result, air drag causes a decrease in the projectile's range and height compared to the ideal projectile motion without air drag.

2. Can air drag be ignored when solving projectile motion problems?

No, air drag cannot be ignored when solving projectile motion problems. While it may be negligible for small and slow moving objects, it becomes increasingly important for larger and faster moving objects. Neglecting air drag can lead to significant errors in the predicted trajectory of a projectile.

3. How do you incorporate air drag into the equations for projectile motion?

The force of air drag can be incorporated into the equations for projectile motion by adding a term for the drag force, which is proportional to the square of the projectile's velocity. This can be done using either the drag coefficient or the cross-sectional area of the projectile, depending on the specific problem being solved. These equations can then be solved using numerical methods or by using computer simulations.

4. What factors influence the amount of air drag on a projectile?

The amount of air drag on a projectile is influenced by several factors, including the object's velocity, mass, shape, and the density and viscosity of the air. Other factors such as temperature, humidity, and altitude can also affect air drag. These factors can be taken into account by using appropriate values for the drag coefficient and cross-sectional area in the equations for air drag.

5. How does air drag impact the maximum height and range of a projectile?

Air drag affects both the maximum height and range of a projectile. The presence of air drag causes the projectile to lose speed and height as it travels, resulting in a lower maximum height and a shorter range compared to the ideal projectile motion. The exact impact of air drag on these parameters depends on the specific conditions of the projectile's motion and the magnitude of the drag force.

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