Question

In the given figure, two objects A and B move towards each other with speeds of $2m{s}^{-1}$ and $8m{s}^{-1}$, the initial distance between them being $20m$. Find the distance covered by both just before they meet each other.

• A. Body A: $4m$ towards right from its initial position.
  Body B: $16m$ towards left from its initial position.
• B. Body A: $12m$ towards right from its initial position.
  Body B: $8m$ towards left from its initial position.
• C. Body A: $10m$ towards left from its initial position.
  Body B: $10m$ towards right from its initial position.
• D. Body A: $6m$ towards right from its initial position.
  Body B: $14m$ towards left from its initial position.

Answer 1

The correct option is A Body A: $4m$ towards right from its initial position.

Body B: $16m$ towards left from its initial position.
Given, speed of body A =$2m{s}^{-1}$,
speed of body B = $10m{s}^{-1}$.
Let the time taken for the two bodies to meet be $t$.
Distance travelled by the body A = $2\times t$.
Distance travelled by the body B = $8\times t$.
Since, the total of the distances travelled $=20m$,
$2t+8t=20$
$\Rightarrow 10t=20$
$\Rightarrow t=2s$.
Distance travelled by the body A = $2\times 2=4m$ towards right from its initial position.
Distance travelled by the body B = $8\times 2=16m$ towards left from its initial position.