capa 4 solutions

# capa 4 solutions - 1 In this question we focus only on one...

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Unformatted text preview: 1) In this question we focus only on one of the three components (say the z-component for instance.) You can therefore neglect the other two (x, and y) and the problem becomes a ‘motion in one dimension’ problem! Then we know how to describe the evolution of the z- component in the case of constant acceleration : z = z + v 0z t + ½ a z t 2 Now, compare the equation given in the problem. Doesn’t it look similar? Remember how the instantaneous velocity is defined (here written as the z-component of a 3-D velocity vector): v z = dz / dt (i.e. the derivative of the position over time). Therefore, we can write for the components given above: v z = v 0z + a z t (Looks familiar? If not, see your lecture notes now!) From the first equation above you now know ‘v 0z ’ and ‘½ a z ’ Put these numbers in the equation above and you find v z . 2) Compare the equation given in your CAPA sheet with the one I wrote above for the z- component of the motion (very first equation on this page). Can you figure out the a z component? Do the same for the a x and a y components (Hint: Some of them could be zero. Don’t forget the ½ in front of a.) Now you know the 3 components of the acceleration vector! Rembember: The magnitude | v | of a 3D vector v with the components x, y, and z is given by (very similar to the Pythagorean relation in 2D): | v | = sqrt( x 2 + y 2 + z 2 ) sqrt: means ‘square root.’ 3) Very similar to last week’s CAPA problem with the medieval knight in vacuum (if you don’t remember it, check the solution of CAPA#3, question 7.)remember it, check the solution of CAPA#3, question 7....
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capa 4 solutions - 1 In this question we focus only on one...

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