You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Examples

A rocket, wit...

Question

A rocket, with an initial mass of 1000 kg, is launched vertically upwards from rest. The rocket burns fuel at the rate of 10 kg per second. The burnt matter is ejected vertically downwards with a speed of 2000 $m s^{- 1}$ relative to the rocket. If burning stops after one minute. Find the maximum velocity of the rocket. (Take g as at 10 $m s^{- 2}$ .

1000 m/s

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1232.6 m/s

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1500.5 m/s

No worries! We‘ve got your back. Try BYJU‘S free classes today!

850.6 m/s

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A 1232.6 m/s
Answer is B.
Using the velocity $v = u - g t + v, l n (\frac{m_{0}}{m})$
Here $u = 0, t = 60 s, g = 10 m / s^{2}, v = 2000 m / s, m_{0} = 1000 k g$
and $m = 1000 - 10 \times 60 = 400 k g$
We get $v = 0 - 600 + 2000 l n (1000 / 400)$
or $v = 2000 l n 2.5 - 600$
= 200{10 In 2.5 - 3) = 1232.6 m/s
Hence, maximum velocity of the rocket is 1232.6 m/s.

Suggest Corrections

Similar questions

Q. A rocket with an initial mass

m = 2000 kg

is launched vertically upwards. The rocket burns fuel at the rate of

20 kg/s

. The burnt material is ejected vertically downwards with a speed of

4000 m/s

relative to the rocket. If burning stops after

30

seconds, find the maximum velocity of the rocket. (Take

g = 10 {m/s}^{2}

)

Q. A rocket with an initial mass of

1000 kg

is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of

10 kg

per second. The burnt matter is ejected vertically downwards with a speed of

2000 m/s

relative to the rocket. If burning ceases after one minute, the maximum velocity of the rocket is

Q. A rocket with an initial mass of

M = 2000 kg

is launched vertically upwards from rest, under gravity. The burnt matter is ejected vertically downwards with a speed of

4000 m/s

relative to the rocket. Velocity of the rocket after

60

seconds is

2000 m/s

. Find the mass of rocket gas ejected in

60

seconds. [Take

g = 10 {m/s}^{2}

]

P S L V

decides to send a rocket to the moon for which it requires a velocity of

1232.6 m/s

after

1 min

. The rocket burns fuel at the rate of

10 kg/s

. The burnt matter is ejected vertically downwards with a speed of

2000 m/s

relative to the rocket. Calculate the initial mass of rocket. [Take

g = 10 {m/s}^{2}

]

P S L V

decides to send a rocket to the moon for which it requires a velocity of

1232.6 m/s

after

1 min

. The rocket burns fuel at the rate of

10 kg/s

. The burnt matter is ejected vertically downwards with a speed of

2000 m/s

relative to the rocket. Calculate the initial mass of rocket. [Take

g = 10 {m/s}^{2}

]

Join BYJU'S Learning Program

The correct option is A 1232.6 m/sAnswer is B.Using the velocity v=u−gt+v,ln(m0m)Here u=0,t=60s,g=10m/s2,v=2000m/s,m0=1000kgand m=1000−10×60=400kgWe get v=0−600+2000ln(1000/400)orv=2000ln2.5−600 = 200{10 In 2.5 - 3) = 1232.6 m/sHence, maximum velocity of the rocket is 1232.6 m/s.