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In this problem, we have three questions.
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First one.
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We are going to find the average velocity in the following situation.
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We are moving with v1 equal to 2 meters per second in the direction 30 degrees east of south for 2 seconds.
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And then we are going with v2 equal to 3 meters per second in the west direction for 3 seconds.
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So what is the average velocity here? now let us consider the following.
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This is east, so we have x, and this is north, so we have y.
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For the first vector, this is s30e.
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So this is 30 degrees and for the second vector west we have this unit vector here okay now let us write down these unit vectors in terms of x and y so s 30 e is equal to sine 30 degrees in the x component and minus cosine 30 degrees in the y component and w is is simply minus 1 in the x component and 0 in the y component.
01:36
Okay, now we write the average velocity using the following formula.
01:43
The change in position over the total duration.
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The change in position here is given by v1 t1 plus v2 t2 divided by delta t is t1 plus theta.
02:00
Now if you compute this vector in the numerator we get minus 7 minus 2 root 3 and in denominator we have 5.
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Okay now let us compute the norm of this vector.
02:17
We have square root of x component squared plus the y component squared.
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So this will give us 1 .56 meters per second.
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And now let us consider the direction.
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We have arc tangent of the absolute value of the y component divided by the x component.
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Okay, we take the absolute value because we are going to decide on direction based on the signs...