A 20,000 kg rocket has a motor that generates 3.0 X 10^5 N of thrust.
a) What is the rocket's initial upward acceleration?
b) At an altitude of 5.0 km the rocket's acceleration has increased to 6.0 m/s^2. What mass of fuel has it burned?
First: calculate the upward net force on the rocket:
Downward force ( weight) = mass * acceleration due to g
Downward force ( weight) = 20,000*9.8 = 196,000N down
Upward force = 300,000N
Net upward force = 300,000- 196,000 = 104,000N
Calculate initial acceleration:
Force(net) = mass * acceleration
Acceleration = Force (net) / mass
Acceleration = 104,000/ 20,000
Acceleration = 5.2m/s2 upwards
At 5km altitude, the force is constant:
calculate mass of rocket:
Force(net) = mass * acceleration
104,000 = mass * 6.0
mass = 104,000/6
mass = 17,333kg
The rocket has burned 20,000 - 17,333 = 2,666.6kg of fuel.