A particle whose speed in 50 m/s moves along the line from A(2, 1) to B(9, 25). Find its velocity vector in the form of `a hat(i) + b hat(j)`.

Options

A. `7hati+24 hatj`
B. `8hati+24 hatj`
C. `14 hati+48 hatj`
D. None of these

Answer

C

Explanation

Position vector of point `A=2hati+hatj`
Position vector point `B=9hati+25 hatj`
`:. vec(AB)=(9hati+25 hatj) -(2hati+hatj)=7hati+24 hatj`
unit vector in the direction of `vec(AB)`
`hat(AB)=(vec(AB))/(|vec(AB)|)=(7hati+24hatj)/25`
`:. vec(v) =50 hat(AB)=14hati+48 hatj`