A particle travels with speed `50ms^(-1)` from the point `(3,-7)` in a direction `7hat(i)-24(j)`. Find its position vector after `3s`.

Options

A. `(45hat(i)-125hat(j))m`
B. `(45hat(i)-151hat(j))m`
C. `(45hat(i)-125hat(j))m`
D. `(35hat(i)-115hat(j))m`

Answer

B

Explanation

Given speed `v= 50 m//s` in the direction `vec(a)= 7hat(i)-24hat(j)`
`vec(v)= vhat(a)` is the unit vector in the direction `7hat(i)-24hat(j)`
`hat(a)= ((7hat(i)-24hat(j)))/(sqrt((24)^(2)+(7)^(2)))=((7hat(i)-24hat(j)))/(25)`
`vec(v)= vhat(a)=50.((7hat(i)-24hat(j)))/(25)= 2(7hat(i)-24hat(j))m//s`
Initially the particle is at `vec(r)_(0)= (3hat(i)-7hat(j))m`
Position of the particle after 3 sec, `vec(r )= vec(r )_(0)+vec(v)t`
`implies vec(r )= (3hat(i)-7hat(j))+3xx2(7hat(i)-24hat(j))= (45hat(i)-151hat(j))m`