Air resistance - find Vx(t) and Vy(t)

In summary: Leave it a day before bumping]In summary, the conversation discusses solving equations to find the velocity components of a football kicked at time t=0, using formulas worked out in class. The equations for Vx(t) and Vy(t) are given, and the problem of integrating them to find x(t) and y(t) is also mentioned. The questioner is unsure of how to incorporate air resistance (k) into the problem, but has initial velocity and acceleration values. They also mention bumping their thread, which is against forum rules.
  • #1
Carnivroar
128
1
Suppose at time t= 0 the football is kicked with initial velocity components Vxo and Vyo. Solve the equations above to find Vx(t) and Vy(t). You can make use of the formulas we worked out in class.

"Equations above":
ax = -kvx
ay = -g-kvy

formula worked in class:

v(t) = (g/k)(1-e^-k(t-to)) + Voe^-k(t-to)

so...

Vx(t) = Vocosθe^-kt

Vy(t) = (9.8m/s^2/k)(1-e^-kt) + Vysinθe^-kt

Is this correct?
 
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  • #2
Next problem is to integrate that to get a formula for x(t) and y(t)

Assuming the above is correct, here's what I got:

x(t) = -V0sin[itex]\theta[/itex]e-k(t-to)/k +V0sin[itex]\theta[/itex]/k

y(t) = -ge-k(t-t0)/k2 + V0cos[itex]\theta[/itex]e-k(t-t0) + g/k2 - V0cos[itex]\theta[/itex]/k
 
  • #3
Please help [URL]http://img.photobucket.com/albums/v253/Hatsuharu1399/gdkifmqq.gif[/URL]
 
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  • #4
Come on guys

Let me rephrase my question

How to I include air resistance (k) into a projectile motion problem?

In this problem, k = 0.1/s

so do I stick that into the acceleration equation to get a new acceleration?

ax = -kVx
ax = -0.1/s * Vx

ay = g - kvy
ay = -9.8m/s^1 - 0.1 * Vy

This part seems okay, but what do I use for Vx and Vy? Is it the initial velocities?

In this problem I was given Vx0 = 12 m/s and ax0 = 10 m/s

So if I use that, I get these constant velocities

ax = -1.2 m/s^2
ay = -10.8 m/s^2
 
  • #5
Carnivroar said:
Please help [PLAIN]http://img.photobucket.com/albums/v253/Hatsuharu1399/gdkifmqq.gif[/QUOTE]
This is considered "Bumping" your thread.

See the https://www.physicsforums.com/showthread.php?t=414380" for these Forums.

Wait 24 hours before bumping your thread.
 
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FAQ: Air resistance - find Vx(t) and Vy(t)

What is air resistance?

Air resistance is the force that opposes the motion of an object through the air. It is caused by the collision of air molecules with the surface of the object.

How does air resistance affect the velocity of an object?

Air resistance acts in the opposite direction of an object's motion, causing it to slow down. This means that the velocity of the object decreases over time in the presence of air resistance.

How do you calculate the air resistance of an object?

The air resistance of an object can be calculated using the formula FR = 0.5 * ρ * v2 * A * CD, where ρ is the density of air, v is the velocity of the object, A is the cross-sectional area, and CD is the drag coefficient.

What is the relationship between air resistance and the speed of an object?

The air resistance on an object increases as the speed of the object increases. This means that the faster an object moves, the greater the air resistance it experiences.

How does air resistance affect the trajectory of an object?

Air resistance has a significant impact on the trajectory of an object. It causes the object to follow a curved path instead of a straight line, as it slows down the object's forward motion and alters its direction.

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