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.