   Chapter 6, Problem 58P

Chapter
Section
Textbook Problem

A spaceship at rest relative to a nearby star in interplanetary space has a total mass of 2.50 × 104 kg. Its engines fire at t = 0, steadily burning fuel at. 76.7 kg/s with an exhaust speed of 4.25 × 103 m/s. Calculate the spaceship’s (a) acceleration at t = 0, (b) mass at t = 125 s, (c) acceleration at t = 125 s, and (d) speed at t = 125 s, relative to the same nearby star.

(a)

To determine
The magnitude of acceleration of the spaceship at time equal to zero seconds

Explanation

Explanation

Given Info:

Mass of the spaceship is 2.50×104kg , rate of fuel burning is 76.7kgs1 , the exhaust speed is 4.25×103ms1 .

Formula to calculate acceleration at time zero seconds is,

a0=TM (I)

• T is the thrust on the spaceship
• M is the total mass of the spaceship

Formula to calculate thrust on the rocket is,

T=|ve(ΔMΔt)| (II)

• ve is the exhaust velocity
• ΔM/Δt is the rate of change of mass of spaceship or fuel

Rewrite t the equation (I) for acceleration using the expression |ve(ΔM/Δt)| for T

a0=|ve(ΔMΔt)|M

Substitute 2

(b)

To determine
The mass of the spaceship at time 125 seconds

(c)

To determine
The magnitude of acceleration at 125 seconds

(d)

To determine
The magnitude speed of the space ship at time 125 seconds

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