A rocket with an initial mass of `1000 kg`, is launched vertically upward 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 . Find the velocity of the rocket after `1 min` of start.
Text Solution
AI Generated Solution
To find the velocity of the rocket after 1 minute, we will use the principles of rocket motion and the conservation of momentum. Here’s a step-by-step solution:
### Step 1: Identify the given data
- Initial mass of the rocket, \( m_0 = 1000 \, \text{kg} \)
- Rate of fuel burn, \( \frac{dm}{dt} = 10 \, \text{kg/s} \)
- Relative velocity of the ejected fuel, \( v_r = 2000 \, \text{m/s} \)
- Time of burn, \( t = 60 \, \text{s} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)
...
A rocket, with an initial mass of 1000kg , is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 10kg per second. The burnt matter is ejected vertically downwards with a speed of 2000ms^-1 relative to the rocket. If burning ceases after one minute, find the maximum velocity of the rocket. (Take g as constant at 10ms^-2 )
A rocket of initial mass m_0 has a mass m_0(1-t//3) at time t. The rocket is lauched from rest vertically upwards under gravity and expels burnt fuel at a speed u relative to the rocket vertically downward. Find the speed of rocket at t=1 .
In a rocket, fuel burns at the rate of 2 kg/s. This fuel gets ejected from the rocket with a velocity of 80 km/s. Force exerted on the rocket is -
In a rocket, fuel burns at the rate of 2 kg/s. This fuel gets ejected from the rocket with a velocity of 80 km/s. Force exerted on the rocket is -
In a rocket, fuel bums at the rate of 1 kg/s. This fuel is ejected from the rocket with a velocity of 60 km/s. This exerts a force on the rocket equal to
A rocket is moving vertically upward against gravity. Its mass at time t is m=m_0-mut and it expels burnt fuel at a speed u vertically downward relative to the rocket. Derive the equation of motion of the rocket but do not solve it. Here, mu is constant.
A rocket consumes 20 kg fuel per second. The exhaust gases escape at a speed of 1000 ms^(-1) relative to the rocket. Calculate the upthrust received by the rocket. Also calculate the velocity acquired. When its mass is 1/100 of the initial mass.
A rocket of mass 20000 kg is ejecting the gases at the rate of 50 kg/sec with speed of 20 m/sec in gravity free space. Find the acceleration of rocket at 2 sec.
A rocket fired from the earth's surface ejects 1% of its mass at a speed of 2000 ms^(-1) in the first second. Find the average acceleration of the rocket in the first second.
A rocket of total mass 1000kg initially is launched from ground. The gases are ejected at the rate 20kg/s with velocity 1000 m/s relative to rocket vertically downwards. The initial acceleration of the rocket is a (in m//s^(2) ). Find a/g . (Take g=10 m//s^(2) )
CENGAGE PHYSICS ENGLISH-CENTRE OF MASS-INTEGER_TYPE
