At time t second, a particle of mass 3 kg has position vector r metre, where `r = 3that(i) - 4 cos t hat(j)`. Find the impulse of the force during the time interval `0 le t le(pi)/(2)`

Options

A. `12hat(j) N-s`
B. `9hat(j) N-s`
C. `4hat(j) N-s`
D. `14hat(j) N-s`

Answer

A

Explanation

`because " "r = 3that(i)-4cost hat(j)`
`therefore " "v=(dr)/(dt)=3hat(i)+4sint hat(j)`
`therefore " "a=(d^(2)t)/(dt^(2))=4costhat(j)`
`therefore " "F = ma = 12 cos t hat(j)`
`therefore " impulse"=int_(0)^(pi//2)F dt`
`=12int_(0)^(pi//2)costdt`
`=12 [sint]_(0)^(pi//2)=12 N-s`
The direction of impulse will be in the direction of force.
`therefore` impulse `= 12 hat(j) N-s`