Question

A fully fueled rocket has a mass of 2100 kg, of which 1500 kg of fuel is burnt and exhausted at the rate of 190 kg at a speed of 2500 m/s relative to the rocket when fired vertically upward. Calculate:

(i) The upthrust of the rocket.

A) 210,000 N
B) 256,000 N
C) 265,000 N
D) 180,500 N

(ii) The net force on the rocket when blasting off.

A) 70,000 N
B) 145,000 N
C) 180,500 N
D) 325,000 N

Answer 1

The upthrust of the rocket is 3,750,000 kg*m/s and the net force on the rocket when blasting off is 3,729,420 N.

Step-by-step explanation:

To calculate the upthrust of the rocket, we need to find the change in momentum of the exhaust gases. The change in momentum is given by the mass of the exhaust gases multiplied by the exhaust velocity. In this case, the mass of the exhaust gases is 1500 kg and the exhaust velocity is 2500 m/s. Therefore, the change in momentum is (1500 kg * 2500 m/s) = 3,750,000 kg*m/s. Since momentum is conserved, the upthrust of the rocket is also 3,750,000 kg*m/s.

To calculate the net force on the rocket when blasting off, we need to subtract the force of gravity from the upthrust. The force of gravity can be found using the equation F = m * g, where m is the mass of the rocket and g is the acceleration due to gravity. In this case, the mass of the rocket is 2100 kg and g is approximately 9.8 m/s^2. Therefore, the force of gravity is (2100 kg * 9.8 m/s^2) = 20,580 N. Subtracting the force of gravity from the upthrust, we get the net force on the rocket as (3,750,000 N - 20,580 N) = 3,729,420 N.