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

Carnivroar

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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Carnivroar

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$\theta$e-k(t-to)/k +V0sin$\theta$/k

y(t) = -ge-k(t-t0)/k2 + V0cos$\theta$e-k(t-t0) + g/k2 - V0cos$\theta$/k

Carnivroar

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Carnivroar

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

SammyS

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