Let `r_(1)(t)=3t hat(i)+4t^(2)hat(j)` and `r_(2)(t)=4t^(2) hat(i)+3that(j)` represent the positions of particles 1 and 2, respectiely, as function of time t, `r_(1)(t)` and `r_(2)(t)` are in metre and t in second. The relative speed of the two particle at the instant t = 1s, will beA. 1m/sB. `3sqrt(2)m//s`C. `5sqrt(2)m//s`D. `7sqrt(2) m//s`

Let `r_(1)(t)=3t hat(i)+4t^(2)hat(j)` and `r_(2)(t)=4t^(2) hat(i)+3tha

1.	Let `r_(1)(t)=3t hat(i)+4t^(2)hat(j)` and `r_(2)(t)=4t^(2) hat(i)+3that(j)` represent the positions of particles 1 and 2, respectiely, as function of time t, `r_(1)(t)` and `r_(2)(t)` are in metre and t in second. The relative speed of the two particle at the instant t = 1s, will beA. 1m/sB. `3sqrt(2)m//s`C. `5sqrt(2)m//s`D. `7sqrt(2) m//s`
Answer» Correct Answer - C Here, `vecr_(1)(t)=3thati+4t^(2)hatj` `vecr_(2)(t)=4t^(2)hati+3thatj` velocity, `vecv_(1)(t)=(dvecr_(1))/(dt)=(d)/(dt)(3t hati+4t^(2)hatj)` `=3hati+8hatj` `vecv_(2)(t)=(dvecr_(2))/(dt)=(d)/(dt)(4t^(2)hati+3t hat j)=8t hati+3 hatj` The relative speed of particle 1 with respect to particle 2 is `vecv_(12)=vecv_(1)-vecv_(2)` `=(3hati+8thatj)-(8thati+3hatj)` `=(3-8t)hati+(8t-3)hatj` At t=1s, `vecv_(12)=(3-8)hati+(8-3)hatj` `=-5hati+5hatj` `\|vecv_(12)\|sqrt((-5)^(2)+(5)^(2))` `=sqrt(25+25)=5sqrt(2) m//s`