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A mass of 1 kg is thrown up with a velocity of 100 m/s. After 5 seconds, it explodes into two parts. One part of mass 400 g comes down with a velocity 25 m/s. Calculate the velocity of other part :
A
40 m/s upward
B
40 m/s downward
C
100 m/s upward
D
60 m/s downward
Detailed Solution
Velocity after 5 seconds (taking g = 10 m/s$^2$): $v = 100 - 10 \times 5 = 50$ m/s upward.
The explosion is due to internal forces, so momentum is conserved just before and just after it. Take upward as $+\hat{j}$:
$1 \times 50\hat{j} = 0.4 \times 25(-\hat{j}) + 0.6\vec{v}$
$50\hat{j} + 10\hat{j} = 0.6\vec{v}$
$\vec{v} = \dfrac{60\hat{j}}{0.6} = 100\hat{j}$ m/s
So the other part moves with 100 m/s upward.
The explosion is due to internal forces, so momentum is conserved just before and just after it. Take upward as $+\hat{j}$:
$1 \times 50\hat{j} = 0.4 \times 25(-\hat{j}) + 0.6\vec{v}$
$50\hat{j} + 10\hat{j} = 0.6\vec{v}$
$\vec{v} = \dfrac{60\hat{j}}{0.6} = 100\hat{j}$ m/s
So the other part moves with 100 m/s upward.