#### Question

# Upward Acceleration and thrust?

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?

#### Answer

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.