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In this lesson, we will learn how to use the rocket equation to calculate the motions of rockets and of the exhaust used to propel them.

Q1:

A large rocket has a mass of 2 . 0 0 × 1 0 6 kg at takeoff, and its engines produce a thrust of 3 . 5 0 × 1 0 7 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?

Q2:

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 3 6 0 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.

Q3:

An unfueled rocket has a mass of 1 3 7 0 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 5 0 0 m/s. What is the minimum mass of fuel that the rocket must be loaded with? Ignore air resistance.

Q4:

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 × 1 0 kg/s with the exhaust moving at a speed of 2 . 5 × 1 0 m/s. The spacecraft’s mass before ejecting any exhaust is 2 . 0 × 1 0 kg.

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

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 = 1 5 s ?

What is the magnitude of the spacecraft’s acceleration at the instant 𝑡 = 3 0 s ?

Q5:

What exhaust speed is required to accelerate A rocket of mass 1 2 0 0 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?

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