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Laws Of Motion

Question
CBSEENPH11017037

A rocket of initial mass 6000 kg ejects mass at a constant rate of 16 kh/s with constant relative speed of 11 km/s. What is the acceleration of the rocket one minute after blast? 

Solution

Here, 
mo = 6000 kg
dm over dt space equals space 16 space k g divided by s
u = 11 km/s = 11000 m/s 
Acceleration,a  = ? 
Time taken, t = =1 min = 60 sec 
Mass left after 1 minute  = mo - (dm/dt) t 
                                      = 6000 - ( 16 x 60)
                                      = 5040 kg
Using the formula, 
F = m. (dv/dt)= u . (dm/dt), we get
a = dv/dt = fraction numerator straight u space left parenthesis thin space dm divided by dt right parenthesis over denominator straight m end fraction space equals space fraction numerator 11000 space straight x space 16 over denominator 5040 end fraction space equals space 34.92 space straight m divided by straight s squared