8. Exercises

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</div>{{#NAVCONTENT:Answer|Answer 8.1|Solution a|Solution 8.1a|Solution b|Solution 8.1b}}
</div>{{#NAVCONTENT:Answer|Answer 8.1|Solution a|Solution 8.1a|Solution b|Solution 8.1b}}
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===Exercise 8.2===
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A particle is set into motion on a smooth inclined plane. The initial velocity of the particle is 5<math>\mathbf{i}</math> <math>\text{m}{{\text{s}}^{-1}}</math>, its acceleration is -4<math>\mathbf{j}</math> <math>\text{m}{{\text{s}}^{-2}}</math> and its initial position is (<math>18\mathbf{i}+14\mathbf{j}</math>) m, where <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are perpendicular unit vectors that lie in the plane in which the particle is moving.
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a) Find the velocity of the particle after it has been moving for 4 seconds.
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b) Find the position of the particle after it has been moving for 8 seconds.
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</div>{{#NAVCONTENT:Answer|Answer 8.2|Solution a|Solution 8.2a|Solution b|Solution 8.2b}}

Revision as of 15:46, 12 September 2009

       Theory          Exercises      


Exercise 8.1


The acceleration of a jet-ski is (\displaystyle 0.9\mathbf{i}+0.7\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-2}}. Its initial velocity is 4\displaystyle \mathbf{i} \displaystyle \text{m}{{\text{s}}^{-1}} and its initial position is (\displaystyle 400\mathbf{i}+350\mathbf{j}) m. The unit vectors are directed east and north respectively.

a) Find the velocity of the jet-ski when t = 10 seconds.

b) Find the position of the jet-ski when t = 10 seconds.


Answer
Answer 8.1
Solution a
Solution 8.1a
Solution b
Solution 8.1b


Exercise 8.2


A particle is set into motion on a smooth inclined plane. The initial velocity of the particle is 5\displaystyle \mathbf{i} \displaystyle \text{m}{{\text{s}}^{-1}}, its acceleration is -4\displaystyle \mathbf{j} \displaystyle \text{m}{{\text{s}}^{-2}} and its initial position is (\displaystyle 18\mathbf{i}+14\mathbf{j}) m, where \displaystyle \mathbf{i} and \displaystyle \mathbf{j} are perpendicular unit vectors that lie in the plane in which the particle is moving.

a) Find the velocity of the particle after it has been moving for 4 seconds.

b) Find the position of the particle after it has been moving for 8 seconds.


Answer
Answer 8.2
Solution a
Solution 8.2a
Solution b
Solution 8.2b
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