A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 34 m/s^2 for 35 s, then runs out of fuel. Ignore any air resistance effects. What is the rocket's maximum altitude? How long is the rocket in the air?

Maximum height = 93005 m

The total time of flight = 294 s

Explanation:

The height during the burning:

s = ut + 0.5at^2  

s = 0.5 x 34 x 35^2  

s = 20825 m

End speed during the burn.

v = u + at = at  

v = 34 x 35

v = 1190 m/s

It rises till the speed is zero:

v = u + at

t = (v - u)/a  

t = -1190/-9.81  

t = 121.3048 s

Maximum height = 20825 + 1190 x 121.308 - 0.5 x 9.81 x 121.3048^2 = Maximum height = 93005 m

Time taken to fall from height

s = 0.5at^2

t^2 = 2s/a

time = SQRT(2s/a) =  

time = SQRT(2 x 93005/9.81)  

Time = 137.7 s

Therefore the total time of flight =  35 +121.3048 + 137.7

Therefore the total time of flight = 294 s

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