Question

heya!
A rocket of initial mass 6000kg ejects mass at a constant rate of 16kg/s with constant relative speed of 11km/s. what is the acceleration of rocket 1 min. after blast?
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Answer 1

Hello guys Namaste,

$m \: of \: object \: = 6000 \: kg$

$\frac{dm}{dt} = 16 \: kg s$

$u = 11 \: km/s$

$t = \: 60 \: s$

In one minute, mass left
mass= m of object - (dm/dt)t
= 6000-(16×60)
= 5040 kg

Now,
F= u dm/dt
= 11×10^3×16
Now,
a= 176×10^3/5040
Acceleration=34.92 m/s^2

Answer 2

Question :

A rocket of initial mass 6000 kg ejects mass at a constant rate of 16kg/s with constant relative speed of 11km/s. What is the acceleration of rocket 1 minute after blast?

Answer :

The acceleration of rocket 1 minute after blast is $\sf{34.92\:m/s^2}$ .

Step-by-step explanation :

Given,

$\sf{m_0=6000}$ kg

$\sf{\frac{dm}{dt}=16}$ kg/s

$\sf{u=11}$ km/s = $\sf{11\times 10^3}$ m/s

$\sf{t=60}$ sec

In one minute i.e., the mass left in 60 sec,

⇒ $\sf{m=m_0-(\frac{dm}{dt})t}$

⇒ $\sf{6000-(16\times 60)}$

⇒ $\sf{5040}$ kg

Since, $\sf{F=u(\frac{dm}{dt})}$

⇒ $\sf{11\times 10^3\times 16}$

⇒ $\sf{176\times 10^3}$

⇒ $\sf{ma=176\times 10^3}$ [$\because$ F=ma]

⇒ $\sf{a=\frac{176\times 10^3}{5040}}$

⇒ $\sf{a=34.92\:m/s^2}$