Worksheet: Rocket Propulsion

In this worksheet, we will practice using the rocket equation to calculate the motions of rockets and of the exhaust used to propel them.


A large rocket has a mass of 2.00×10 kg at takeoff, and its engines produce a thrust of 3.50×10 N.

Find the rocket’s initial vertically upward acceleration.

How much time is required for the rocket to attain a vertically upward velocity of 33.33 m/s, assuming constant mass and thrust?


What exhaust speed is required to accelerate A rocket of mass 1,200 kg is in deep space. The rocket accelerates from a speed of 0.80 km/s to a speed of 1.0 km/s in a time of 5.0 s. Using 50 kg of fuel, what must be the exhaust speed to produce this acceleration?


A rocket accelerates vertically upward and reaches a speed of 132 m/s. Rocket fuel is burned, expelling 115 kg of exhaust from the rocket vertically downward at 1,360 m/s. The time taken for the rocket to complete its acceleration was 12.4 s. What was the mass of the rocket when fully loaded with fuel? Ignore air resistance.


An unfueled rocket has a mass of 1,370 kg. The rocket must be loaded with sufficient fuel to reach a vertically upward speed of 677 m/s after 25.0 s of acceleration. The rocket ejects exhaust from burned fuel vertically downward at 1,500 m/s. What is the minimum mass of fuel that the rocket must be loaded with? Ignore air resistance.


A spacecraft is moving uniformly in deep space where gravitational forces are negligible. At the instant 𝑡, the spacecraft’s engine is activated for a 30 s time interval, during which exhaust is ejected from the spacecraft at a rate of 2.0×10 kg/s with the exhaust moving at a speed of 2.5×10 m/s. The spacecraft’s mass before ejecting any exhaust is 2.0×10 kg.

What magnitude force is applied to the spacecraft by the engine while it is activated?

  • A 5 . 0 × 1 0 N
  • B 5 . 5 × 1 0 N
  • C 2 . 2 × 1 0 N
  • D 2 . 0 × 1 0 N
  • E 4 . 0 × 1 0 N

What is the magnitude of the spacecraft’s acceleration at the instant 𝑡?

What is the magnitude of the spacecraft’s acceleration at the instant 𝑡=15s?

What is the magnitude of the spacecraft’s acceleration at the instant 𝑡=30s?

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