Question

A body is projected from the ground with an upward velocity of $100\text{m/s}$. The body explodes into two fragments of mass $m$ and $2m$ just after it was projected. If the lighter part comes to rest instantly, find the maximum height attained by the other part.[Take $g=10{\text{m/s}}^2$]

• A. $1125\text{m}$
• B. $1500\text{m}$
• C. $100\text{m}$
• D. $1250\text{m}$

Answer 1

The correct option is A $1125\text{m}$

Masses of the two fragments are $m$ and $2m$ and velcoity of the lighter part after explosion is zero.
Now, applying momentum conservation (taking velocity of heavier part as $v$) :
$(m+2m)100=m\times 0+2mv$
$\Rightarrow 300m=2mv$
$\Rightarrow v=150\text{m/s}$

Then, maximum height attained by the heavier part $=\frac{v^2}{2g}=\frac{{150}^2}{2g}$
$\therefore H_{\text{max}}=1125\text{m}$