Question

Two particles having the position ${\overline{r}}_1=(3\hat{i}+5\hat{j})m$ and ${\overline{r}}_2=(-5\hat{i}-3\hat{j})m$ move with velocities ${\overline{V}}_1=(4\hat{i}+3\hat{j})m/s$ and ${\overline{V}}_2=(a\hat{i}+7\hat{j})m/s$ . If the particles collide, then value of a must be :

• A. 8
• B. 6
• C. 4
• D. 2

Answer 1

The correct option is A 8

given the points and their velocities coordinates after 't' time will be
(4t+3 , 3t+5) and (at-5 , 7t-3), for collision all the coordinates must be equal at some time.
equating Y-coordinates gives us $7t-3=3t+5t=2sec$
at $t=2$ X - coordinates. $4t+3=at-54\times 2+3=2a-5a=8$