Question

A jogger runs directly east for 3 km, then turns and goes northwest for 5 km. He then travles directly south for 4 km. How fair is he from the starting point? (km)

In what direction is he from the starting point (measured as an angle counterwise from the east axis, units are deg)? (Northwest is the direction lying exactly half way between north and west.)

Answer 1

If you draw a diagram to a scale this problem is very easy to do. Else you could take the components of each vector and add them up.

east 3km
=> horizontal component = +3km
=> vertical component = 0

north west 5km
=> horizontal component = - 5 * cos (45) = - 3.53 km
=> vertical component = 5 * sin (45) = 3.53 km

south 4km
=> horizontal component = 0
=> vertical component = - 4 km

adding vectors,

=> horizontal component = 4 - 3.53 = 0.46km
=> vertical component = 3.53 - 4 = -0.46km

1.
therefore the distance from the starting point = sqrt (0.46 ^2 + (-0.46) ^2) = 0.65km

2.
tan^-1 (0.46/0.46) = 45 clockwise from east axis. 315 counter clockwise from east axis