A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 60.4 × 105 kg, of which 3.51 × 105 kg is fuel. The rocket engine is then fired for 380 s, during which fuel is consumed at the rate of 490 kg/s. The speed of the exhaust products relative to the rocket is 2.36 km/s. (a) What is the rocket's thrust? After the 380 s firing, what are (b) the mass and (c) the speed of the rocket?

a The rocket's thrust is

b The mass of the rocket

c  The speed of the rocket

Explanation:

From the question we are told that

            The mass of Rocket  is  

             The mass of fuel is

            The duration the rocket engine was fired  

            The rate at  which fuel was consumed

  The speed of the exhaust product is  

Generally Thrust can be  represented as

   Substituting values

  The mass of fuel consumed in 380 s would  be

                 Rate of  fuel consumption * The the time taken (The duration the rocket engine was fired)

               =  490 × 380 = 186200 kg

  So the new mass of rocket would be

Generally velocity of a rocket can be mathematically represented as

where is the speed of the exhaust

            is the initial mass of the rocket

          is the final mass of the rocket

the total distance traveled by the car is

30km + 49km = 79 km .

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s