Question

A rocket has a mass of 21000 kg of which 15000 kg is fuel. The rocket engine can exhaust fuel at
the rate of 1
190kg s
with an exhaust velocity 1
2500ms
relative to the rocket. If the rocket is fired
vertically upwards, its final velocity at the burn out is (in 1
ms

) [ ]
a) 2735 b) 2935 c) 2535 d) 1975

Answer 1

Answer:

b

Explanation:

thank you for your time and consideration

Answer 2

Given:

A rocket has a mass of 21000kg of which 15000kg is fuel. The rocket engine can exhaust fuel at the rate of 190kg per second with an exhaust velocity 2800metre per second relative to the ground.

To find:

If the rocket is fired upwards final velocity at the burn out is?

Solution:

From given, we have,

A rocket has a mass of 21000kg of which 15000kg is fuel.

⇒ M = 21,000 kg

⇒ m = 15000 kg

The rocket engine can exhaust fuel at the rate of 190kg per second with an exhaust velocity 2800metre per second relative to the ground.

⇒ dm = 190 kg/s

⇒ 2800 m/s

The formula used to calculate the time taken is,

t = m/dm

where m is the mass and dm is the change in mass

substitute the given values in the above equation.

t = 15,000/190

t = 78.94 ≈ 79 s

The velocity of the rocket after time "t" is given by the formula,

v = u - gt + v_r log [(M - m) / M]

v = 0 - (9.8 × 79) + (-2800) log [(21,000 - 15,000) / 21,000]

v = -774.2 - 2800 (-0.544)

v = -774.2 + 1523.3

v = 749.1 km/s