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Chapter 11: Q. 36 (page 288)

A rocket in deep space has an empty mass of 150 kg and exhausts the hot gases of burned fuel at 2500 m/s. What mass of fuel is needed to reach a top speed of 4000 m/s?

Short Answer

Expert verified

The mass of fuel needed to reach the maximum speed is593kg.

Step by step solution

01

Step 1. Given information

Mass of rocket, mR=150kg

speed of exhaust gas, vex=2500m/s

maximum speed,vmax=4000m/s

02

Step 2. Analyze

When the fuel is entirely burnt, the rocket exceeds the threshold speed. As a result, the entire quantity of the fuel has been used, and we have reached our goal. The rocket's maximum speed is calculated using an equation of the type

vmax=vexlnmR+mF0mRvmaxvex=lnmR+mF0mRevmaxvex=mR+mF0mRmF0=mRevmax/vex-1

03

Step 3. Evaluate

Substitute and evaluate,

mF0=mRevmax/vex-1mF0=150e4000/2500-1=593kg

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