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

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Homework Help Overview

The discussion revolves around finding the velocity vector of a projectile given its acceleration vector, which includes a term for air resistance. The problem involves integrating the acceleration function a(t) to derive the velocity function v(t), with specific initial conditions provided.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the integration of the acceleration vector a(t) and the implications of the initial conditions, particularly the initial velocity v(0). Some express confusion about handling constants during integration and the presence of the term +160 in the integration process.

Discussion Status

The discussion is ongoing, with participants sharing their attempts at integration and questioning how to manage constants. Some have noted that θ and V0 are constants, while others are seeking clarification on the integration process and the constants of integration.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may include specific rules about how to approach the problem and the need to consider air resistance in the model.

ShakeECET109
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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
 
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θ is just a constant, so it should be easy to integrate a(t) .
 
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]
 
Last edited by a moderator:
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
 
theta and V0 are constants
 
anyone?? really need help on this
 
How did you get rid of your constants of integration?
 
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
 
ShakeECET109 said:
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.
 

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