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Chapter 9: Problem 25

You're working in mission control for an interplanetary space probe. A trajectory correction calls for a rocket firing that imparts an impulse of \(5.64 \mathrm{N} \cdot \mathrm{s}\). If the rocket's average thrust is \(135 \mathrm{mN},\) how long should the rocket fire?

Short Answer

Expert verified
After carrying out the calculation, we find that the rocket should fire for around 41.78 seconds.

Step by step solution

01

Understand the Problem

The problem is asking to find how long the rocket should fire. We're given the impulse which is \(5.64 \mathrm{N} \cdot \mathrm{s}\) and the rocket's average thrust which is \(135 \mathrm{mN}\). The force equals the rocket's average thrust so we can say that \(F = 135 \mathrm{mN} = 0.135 \mathrm{N}\). The impulse is 'I' which equals \(5.64 \mathrm{N} \cdot \mathrm{s}\). We know that impulse \(I = F \cdot \Delta t\), where \( \Delta t\) is the time for which the rocket fires.
02

Substitute the known values into the equation

We substitute the known values into the impulse equation \(I = F \cdot \Delta t\), and rearrange it to solve for \( \Delta t\). Which gets us \( \Delta t = I / F \).
03

Calculate the Time

Substitute the values into the equation we have \( \Delta t = 5.64 \mathrm{N} \cdot \mathrm{s} / 0.135 \mathrm{N}\). The Newton units cancel out leaving us with time in seconds.
04

Final Answer

Perform the division to find the value of \( \Delta t\) which is the time for which the rocket should fire.

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