Question

A shell of mass $100g$ moving with speed of $50m{s}^{-1}$ along a straight line inclined at an angle ${\tan }^{-1}\left(\frac{4}{3}\right)$ to the horizontal bursts into two pieces. The piece of mass $60g$ starts moving horizontally with a speed of $50m{s}^{-1}$. The other piece moves with a speed of

• A. $50m{s}^{-1}$ opposite to the first piece
• B. $100m{s}^{-1}$ in vertically downward direction
• C. $50m{s}^{-1}$ in the same direction as the first piece
• D. zero (remains at rest)

Answer 1

Answer: (B)

Initial momentum
$=\frac{100}{1000}\times 50kgm{s}^{-1}=5kgm{s}^{-1}$
Horizontal momentum $=3kgm{s}^{-1}$
Vertical momentum $=4kgm{s}^{-1}$
The velocity of other piece of mass $40g$
$=\frac{4kgm{s}^{-1}}{0.04kg}=100m{s}^{-1}$

To conserve momentum, it should be directed vertically downward