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Chapter 9: Q76P (page 253)

A 6090 kgspace probe moving nose-first toward Jupiter at 105 m/srelatives to the Sun fires its rocket engine, ejectingof exhaust at a speed of 253 m/srelatives to the space probe. What is the final velocity of the probe?

Short Answer

Expert verified

Final velocity of the probe is 108m/s.

Step by step solution

01

Listing the given quantities

Mass of the space probe isMi=6090kg

Mass of the exhaust isMe=80kg

Speed of the exhaust relative to the space probe is,vrel=253m/s

Initial speed of the space probe is,vi,s=105m/s

02

Concept

Using the second rocket equation we can find the final velocity of the probe.

Formula:

Second rocket equation gives,

vf-vi=vrelInMiMf

03

Calculation of final velocities

Final mass of the system

Mi-Me=6090-80=6010kg

Initial speed of the system is,

vi=vi,s+vi,e=105m/s+0=105m/s

Second rocket equation gives,

vf-vi=vrelInMiMf=105+253In60906010=108.35~108m/s

Therefore, Final velocity of the probe is 108 m/s

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