Question

The distance between two particle is decreasing at the rate of 6 m/sec. If these particles travel with same speeds and in the same direction, then the separation increase at the rate of 4 m/sec. The particle have speed as

• A. 5 m/sec ; 1 m/sec
• B. 4 m/sec ; 1 m/sec
• C. 4 m/sec ; 2 m/sec
• D. 5 m/sec ; 2 m/sec

Answer 1

The correct option is A 5 m/sec ; 1 m/sec

Let the velocities be v and v’ respectively

Now, when the distance between two particles is decreasing we will have

$v+v^{\prime }=6m/s$

$v=6-v^{\prime }....\left(I\right)$

And when the distance is decreases

$v-v^{\prime }=4m/s$

$v=4+v^{\prime }.....\left(II\right)$

Now, from equation (I) and (II)

$4+v^{\prime }=6-v^{\prime }$

$2v^{\prime }=2$

$v^{\prime }=1m/s$

Now, put the value of v’ in equation (II)

$v=4+1$

$v=5m/s$

Hence, the velocities $1m/s$ and $5m/s$