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Chapter 2: Q118CE (page 71)

Question: A rocket maintains a constant thrust F, giving it an acceleration of g

(i.e.,9.8m/s2).

(a) If classical physics were valid, how long would it take for the rocket鈥檚 speed to reach 0.99c??

(b) Using the result of exercise 117(c), how long would it really take to reach 0.99c??

u=11+(Ft/mc)2FTt

Short Answer

Expert verified
  1. If classical approximations were valid for high speeds,it would take almost a year for the rocket to reach 0.99c,
  2. But in reality o.e., relativistic-ally,it would take around seven years.

Step by step solution

01

Determine the time required to reach 0.99 cclassically

(a) Using classical kinematic equations,

v=u+at

Let鈥檚 consider the rocket was initially at rest, and then due to constant thrust, it traveled at an acceleration of g.

v=gtt=vgt=0.99脳3脳108ms9.8ms2t=3.03脳107s

Therefore, classically,the time required to reach the velocity of is0.96 years or around350 days.

02

Determine the time required to reach 0.99 crelativistically

(b) Now,relativistic-ally,

u=11+(Ft/mc)2FTt=muF1+Ftmc2t2=muF21+Ftmc2

Here, F=ma=mg

t2=ug21+gtc2

Rearranging further to get an equation for t ,

t=ug1-u2c2=0.99c9.8ms21-(0.99)2=2.143脳108s=6.795yrs

.

Hence, the time the rocket really takes to reach 0.99cis6.8years.

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