# Physics: Vectors

A hiker walks 10.0 km[NE], 5.0 km[W], and then 2.0 km[S] in 2.5 h.

(a) What is the hiker's displacement?
(b) In what direction must the hiker set out, in order to return by the most direct route to the starting point?
(c) If the hiker walks at a constant speed for the entire trip and returns by the most direct route, how long will the total walk take?

Thanks!

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1. Let the starting point be in the origin of coordinate system. Then the points of the hicker’s route are A , B and C.
AB=10 => A (7.1; 7.1),
BC =5 => B(2.1; 7.1),
BC=2 => C (2.1; 5.1)
Displacement BC = sqrt(2.1²+5.1²)=5.22 km
The angle with +x-axis is arctan(5.1/2.1)=67.6º
s=10+5+2=17 km,
v=s/t=17/2.5 =6.8 km/h
L=10+5+2+5.22 =22.22 km,
t1=L/v=/6.8=3.27 h.

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