# Homework Help: Air resistance - find Vx(t) and Vy(t)

1. Sep 29, 2011

### 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?

2. Sep 29, 2011

### 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

3. Sep 29, 2011

### Carnivroar

Last edited by a moderator: Apr 26, 2017
4. Sep 29, 2011

### 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

5. Sep 29, 2011

### SammyS

Staff Emeritus

Last edited by a moderator: May 5, 2017