Question

From a tower of height $20m$ two identical particles are projected. One in horizontal direction with velocity $2m/s$. and another one is just dropped. When the second particle hit the ground. Coordinate of $C.M$ w.r.t projection point is:

• A. $(2,-20)$
• B. $(2,20)$
• C. $(-2,20)$
• D. $(-2,-20)$

Answer 1

The correct option is A $(2,-20)$

Both particles have $same$ $vertical$ velocity i.e $zero$ so they will reach simultaneously.

Taking the projection point at $origin$ and the $horizontal$ direction as $x$ $axis$ we get that both particles will have their

y coordinate as $y_1=-20m=y_2$

and the x coordinate of $second$ particle will be $x_2=0\left(beneath\right)$

and the time taken by the first particle in covering $20m$ will be $t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\times 20}{10}}=2sec$

Horizontal distance covered in this time will be $u\times t=2m/s\times 2s=4meter$

so the x coordinate of the first particle will be $x_1=4m$

coordinate of center of mass $x=\frac{m{x}_1+m{x}_2}{m+m}=2$

similarly $y=-20$ so we get center of mass as $(2,-20)$