Find v(t) the velocity vector of a projectile given a(t).

[ShakeECET109]

Homework Statement

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

Homework Equations

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

 

[SammyS]

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

 

[ShakeECET109]

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

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

 

[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

 

[ShakeECET109]

theta and V0 are constants

 

[ShakeECET109]

anyone?? really need help on this

 

[SammyS]

How did you get rid of your constants of integration?

 

[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

 

[SammyS]

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 still confused on this problem

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.