Question

1.

A student bikes to school by traveling first dN = 1.00miles north, then dW = 0.500miles west, and finally dS = 0.200miles south.

If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the school, what distance db would the bird cover?

Express your answer in miles.

2.

You will now find the same quantity algebraically, without the need to use much geometry. Take the north direction as the positive y direction and east as positive x. The origin is still where the student starts biking.

Let d? N be the displacement vector corresponding to the first leg of the student's trip. Express d? N in component form.

Express your answer as two numbers separated by a comma (e.g., 1.0,2.0). By convention, the x component is written first.

Answer 1

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A student bikes to school by traveling first d_N = 0.800 \rm {miles} north, then d_W = 0.300 \rm {miles} west, and finally d_S = 0.100 \rm {miles} south.

If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the school, what distance d_b would the bird cover?   

answer 1)

we have 3 vectors and find the sum will give u the answer

v1 = + .8 j

v2= - .3 i

v3= - .1 j

v(sum) = v1+v2+V3 = .3i + (.8 - .1) j = .3 i + .7 j

distance = |v(sum) | = ?.3^2+.7^2 = .7615

answer 2)

1 mile in +y direction
0 in x direction
hence component is (0,1)

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