First slide

Second law

Question

A rocket of initial mass 6000kg ejects mass at constant rate of 200 kg/sec. with constant relative speed of 800 m/sec. The acceleration of the rocket after 5 sec is (neglect gravity)

Moderate

A

50 m/s²
B

16 m/s²
C

60 m/s²
D

32 m/s²

Solution

$F = u\left( {\frac{{dm}}{{dt}}} \right) = ma\;\& \;m = {m_0} - \left( {\frac{{dm}}{{dt}}} \right)t$
$(800)(200) = (6000 - 200 \times 5)a$
$5\cancel{{000}}(a) = 80\cancel{0} \times 2\cancel{{00}}$
$a = \frac{{160}}{5} = 32\,m/{s^2}$

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