The propellant in a single stage sounding rocket occupies $60 \%$ of its initial mass. If all of it is expended instantaneously at an equivalent exhaust velocity of $3000 \mathrm{~m} / \mathrm{s}$, what would be the altitude attained by the payload when launched vertically? [Neglect drag and assume acceleration due to gravity to be constant at $\left.9.81 \mathrm{~m} / \mathrm{s}^{2} .\right]$

(A) $315 \mathrm{~km}$

(B) $335 \mathrm{~km}$

(C) $365 \mathrm{~km}$

(D) $385 \mathrm{~km}$

The propellant in a single stage sounding rocket occupies $60 \%$ of its initial mass. If all of it is expended instantaneously at an equivalent exhaust velocity of $3000 \mathrm{~m} / \mathrm{s}$, what would be the altitude attained by the payload when launched vertically? [Neglect drag and assume acceleration due to gravity to be constant at $\left.9.81 \mathrm{~m} / \mathrm{s}^{2} .\right]$

(A) $315 \mathrm{~km}$

(B) $335 \mathrm{~km}$

(C) $365 \mathrm{~km}$

(D) $385 \mathrm{~km}$

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