# Homework Help: Find v(t) the velocity vector of a projectile given a(t).

1. Sep 28, 2011

### ShakeECET109

1. The problem statement, all variables and given/known data

Suppose we have a projectile launched from an initial height of h ft with initial speed V0 ft/sec and angle of elevation theta. We will attempt to model air resistance by assuming acceleration vector given by...

a(t)= (-.2)(V0)cos(theta)e^(-.2t)i-(.2)((V0)sin(theta)+160))e^(-.2t)j

2. Relevant equations

3. The attempt at a solution

I know I need to integrate this equation, but I am not getting the correct value.
The teacher gave us a hint that v(0)=(V0)cos(theta) i+ (v0)sin(theta) j

2. Sep 28, 2011

### SammyS

Staff Emeritus
θ is just a constant, so it should be easy to integrate a(t) .

3. Sep 28, 2011

### ShakeECET109

i component
[PLAIN]http://www4b.wolframalpha.com/Calculate/MSP/MSP27119ha2d01ca4299bi000030d6c3af4h784902?MSPStoreType=image/gif&s=32&w=352&h=34 [Broken]

j component
[URL]http://www2.wolframalpha.com/Calculate/MSP/MSP477919ha2b5d070h1318000054ch856h732hh6ac?MSPStoreType=image/gif&s=16&w=442&h=34][/URL]

Last edited by a moderator: May 5, 2017
4. Sep 28, 2011

### ShakeECET109

I can integrate it but the teacher said

Find the velocity vector of the projectile (remember that v(0)= V0*cos(theta)i+V0sin(theta)j

every time I integrate a(t) to get v(t) then plug t=0 I cannot get rid of the +160

5. Sep 28, 2011

### ShakeECET109

theta and V0 are constants

6. Sep 28, 2011

### ShakeECET109

anyone?? really need help on this

7. Sep 28, 2011

### SammyS

Staff Emeritus
How did you get rid of your constants of integration?

8. Sep 28, 2011

### ShakeECET109

I did not get rid of the constants V0 and theta I just put them outside of the integral. I got a couple similar answers, but I did not understand the comment he put under the question. I am stiff confused on this problem

9. Sep 29, 2011

### SammyS

Staff Emeritus
Those are not constants of integration.

When you find an anti-derivative there is a constant of integration, usually C, that is added to the result.