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

**Q2: **

What exhaust speed is required to accelerate A rocket of mass 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?

**Q3: **

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 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.

**Q4: **

An unfueled rocket has a mass of 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 m/s. What is the minimum mass of fuel that the rocket must be loaded with? Ignore air resistance.

**Q5: **

A spacecraft is moving uniformly in deep space where gravitational forces are negligible. At the instant , the spacecraft’s engine is activated for a 30 s time interval, during which exhaust is ejected from the spacecraft at a rate of kg/s with the exhaust moving at a speed of m/s. The spacecraft’s mass before ejecting any exhaust is kg.

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

- A N
- B N
- C N
- D N
- E N

What is the magnitude of the spacecraft’s acceleration at the instant ?

What is the magnitude of the spacecraft’s acceleration at the instant ?

What is the magnitude of the spacecraft’s acceleration at the instant ?