Question

A student bikes to school by traveling first dn = 1.00 miles north, then dw = 0.400 miles west, and finally ds = 0.100 miles south.

Answer 1

Here student moves as

`d_n = 1 miles` North

`d_w = 0.4 miles` West

`d_s = 0.1 miles` South

Now total distance moved by the student is just the algebraic sum of all

So it is

`d = d_n + d_w + d_s = 1 + 0.4 + 0.1 = 1.5 miles`

So here we can also find the displacement

displacement is the straight line distance between initial and final position

so net displacement here towards north direction is given as

`d_n = 1 - 0.1 = 0.9 miles` North

net displacement towards west is

`d_w = 0.4 miles`

now the net displacement will be given by Pythagoras Theorem

`d = √(d_n^2 + d_w^2)`

`d = √(0.9^2 + 0.4^2) = 0.98 miles`

and direction is given as

`\theta = tan^(-1)(0.9)/(0.4)`

`\theta = 66 deree` North of west