- #1
cscott
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I this how you would describe projectile motion in terms of DE's?
[tex]\frac{dy}{dt} = 25.0 - gt[/tex]
[tex]\frac{dx}{dt} = 10.0[/tex]
[tex]\frac{dy}{dt} = 25.0 - gt[/tex]
[tex]\frac{dx}{dt} = 10.0[/tex]
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arildno said:No. For one, "g" doesn't equal 9.8 in most common choices of units.
dav2008 said:Well if your initial velocities (25 and 10) are given in m/s then there's no problem of using 9.8 for g.
Consider your actual question. Nowhere did you state what 25.0 or 10.0 represent, and you wanted an answer for a GENERAL description of projectile motion in terms of D.E.cscott said:I this how you would describe projectile motion in terms of DE's?
[tex]\frac{dy}{dt} = 25.0 - gt[/tex]
[tex]\frac{dx}{dt} = 10.0[/tex]
Projectiles with DE's (differential equations) refer to the mathematical models used to describe the motion of objects through the air, taking into account factors such as gravity, air resistance, and initial velocity.
Differential equations are important in projectile motion because they allow us to accurately predict the path and landing point of a projectile. Without taking into account the various forces acting on the object, our predictions would be less precise.
To solve projectile motion problems, we first identify the known values such as initial velocity, angle of launch, and air resistance. We then use these values to set up a differential equation that represents the motion of the object. Finally, we use mathematical techniques such as integration to solve for the unknown variables.
Projectiles with DE's have numerous real-life applications, such as predicting the trajectory of a rocket launch, designing projectiles for military use, and understanding the behavior of objects in sports like baseball or golf.
While differential equations provide accurate predictions for most projectile motion problems, they do have some limitations. For example, they do not take into account factors such as wind or air turbulence, which can affect the trajectory of a projectile. Additionally, they assume a uniform and idealized environment, which may not always be the case in real-life scenarios.