Question

Two bodies are projected simultaneously from the same point, in the same vertical plane, one towards east and other towards west with velocities $8m{s}^{-1}$and $2m{s}^{-1}$ respectively. The time at which their velocities are perpendicular to each other is

• A. $\frac{2}{5}s$
• B. $\frac{3}{5}s$
• C. $1s$
• D. $2s$

Answer 1

The correct option is A $\frac{2}{5}s$

As both the projectices are moving under gravity there horizontal component of velocity will remain coefficient and verticle component will keep on increasing.

Let velocity of projectiles in vertical direction is $V$ after time t.

If both moves perpendicular then

$Tan{\theta }_1=\frac{V}{8},Tan{\theta }_2=\frac{V}{2}$

And ${\theta }_1+{\theta }_2=90°$

$Tan{\theta }_1=\frac{1}{2},Tan{\theta }_2=2$

So $V=4$

As we know $u=0,v=4,a=10$

Then using v=u+at

We get t=0.4sec

So best possible answer is option A .