Some exercise questions about Tsiolkovsky's Rocket Equation and Thrust Equation

I have found 6 of the question’s answers, but I don’t know they are correct. The last question about time of the burn I get negative result -0.42 seconds. Time could not be a negative value, so I checked my answer more than 10 times but can’t get where I do mistake.

Questions

My Answers

1st question’s answer is,

$$1atm = P{_{o}} = 101300Pa$$
$$F{_{nozzle}} = (P{_{e}} – P{_{o}}) cdot A{_{e}}$$
$$F{_{nozzle}} = (101325 – 101300) cdot 1 = 25N$$

2nd question’s answer is,

$$Po = 0Pa$$
$$F{_{nozzle}} = (P{_{e}} – P{_{o}}) cdot A{_{e}}$$
$$F{_{nozzle}} = (101325 – 0) cdot 1 = 101325N$$

3rd question’s first answer is,

$$F{_{nozzle}} = 25N, dot{m} = 1kg/sec, v{_{e}} = 400m/sec$$
$$F{_{thrust}} = dot{m}v{_{e}} + (P{_{e}} – P{_{o}}) cdot A{_{e}}$$
$$F{_{thrust}} = dot{m}v{_{e}} + F{_{nozzle}}$$
$$F{_{thrust}} = 1 cdot 400 + 25 = 425N$$

3rd question’s second answer is,

$$F{_{nozzle}} = 101325N, dot{m} = 1kg/sec, v{_{e}} = 400m/sec$$
$$F{_{thrust}} = dot{m}v{_{e}} + (P{_{e}} – P{_{o}}) cdot A{_{e}}$$
$$F{_{thrust}} = dot{m}v{_{e}} + F{_{nozzle}}$$
$$F{_{thrust}} = 1 cdot 400 + 101325 = 101725N$$

4th question’s answer is,

$$I{_{sp}} = 363sec, I = 2MN = 2000000N$$
$$C = g cdot I{_{sp}}$$
$$C = 9,8 cdot 363 = 3557,4m/s$$

5th question’s answer is,

$$I{_{sp}} = 363sec, I = 2MN = 2000000N, C = 3557,4m/sec$$
$$F{_{thrust}} = dot{m} cdot C$$
$$dot{m} = frac{F{_{thrust}}}{C}$$
$$dot{m} = frac{2000000}{3557} = 562,2kg/sec$$

6th question’s answer is,
$$I{_{sp}} = 363sec, I = 2MN = 2000000N, C = 3557,4m/sec, dot{m} = 562,2kg/sec, Delta v = 7700m/sec$$
$$frac{M{_{full}}}{M{_{empty}}} = e^{frac{Delta v}{C}}$$
$$frac{M{_{full}}}{M{_{empty}}} = e^{frac{7700}{3557,4}} = 8,7$$
$$MR = 8,7$$

7th question’s answer is,

$$I{_{sp}} = 363sec, I = 2MN = 2000000N, C = 3557,4m/sec, dot{m} = 562,2kg/sec, Delta v = 7700m/sec, MR = 8,7$$
$$t{_{b}} = ln(frac{M{_{full}}}{M{_{empty}}}) cdot I{_{sp}} – frac{Delta v}{g}$$
$$t{_{b}} = ln(8,7) cdot 363 – frac{7700}{9,8} = -0,42sec??$$

Why the 7th question’s answer is coming negative value as a time value? Also, are other answers are true?

Thanks!