A car travles 6km towards north at an angle of `45^(@)` to the east and then travles distance of 4km towards north at an angle of `135^(@)` to east (figure). How far is the point from the starting point? What angle does the straight line joining its initial and final position makes with the east?

Options

A. `sqrt(50)` km and `tan^(-1)(5)`
B. 10 km and `tan^(-1)sqrt(5)`
C. `sqrt(52)` km and `tan^(-1)(5)`
D. `sqrt(52)` km and `tan^(-1)sqrt(5)`

Answer

c

Explanation

S= Displacement =AC=`sqrt(6^(2)+4^(2))=sqrt(52)`km
angle between AC and AB =`tan^(-1)(BC)/(AB)`
[using tan (A+B)=`(tan A+tan B)/(1-tan A tan B)`]