- Home
- Standard 11
- Physics
A rocket is moving in a gravity free space with a constant acceleration of $2 \ ms ^{-2}$ along $+x$ direction (see figure). The length of a chamber inside the rocket is $4 \ m$. A ball is thrown from the left end of the chamber in $+x$ direction with a speed of $0.3 \ ms ^{-1}$ relative to the rocket. At the same time, another ball is thrown in $-x$ direction with a speed of $0.2 \ ms ^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is:
$2$
$3$
$4$
$5$
Solution
consider motion of two balls with respect to rocket
Maximum distance of ball A from left wall $=\frac{ u ^2}{2 a }=\frac{0.3 \times 0.3}{2 \times 2}=\frac{0.09}{4} \approx 0.02 m$ so collision of two balls will take place very near to left wall
For $B \quad S = ut +\frac{1}{2} a t^2$
$\quad-4=-0.2 t-\left(\frac{1}{2}\right) 2 t^2 \quad \Rightarrow \quad t^2+0.2 t-4=0 $
$\Rightarrow \quad t=\frac{-0.2 \pm \sqrt{0.04+16}}{2}=1.9 $
$\text { nearest integer }=2 s$
