Question #91269
the fastest propeller - driven aircraft is the Russian TU- 95/142, which can reach a maximum speed of 925km/h for this speed, calculate the planes resultant displacement if it travels due east for 1.50h, then turns N45 degree East and travels for 2.0h (d= 1.32 × 10 rise to power of six meter, Φ= N3.5 degree East)
1
Expert's answer
2019-07-11T09:28:18-0400

Using law of cosines, square of total displacement is

(9251.5)2+(9252)22(9251.5)(9252)cos(18045)=(925*1.5)^2+(925*2)^2-\newline -2*(925*1.5)*(925*2)*cos(180-45)=

(9251.5)2+(9252)22(9251.5)(9252)(2)/2=(925*1.5)^2+(925*2)^2-\newline -2*(925*1.5)*(925*2)*(-\sqrt{\smash[b]{2}})/2=

(9251.5)2+(9252)2++(9251.5)(9252)(2)=(925*1.5)^2+(925*2)^2+\newline +(925*1.5)*(925*2)*(\sqrt{\smash[b]{2}})=

9252(1.52+22+1.522)925^2*(1.5^2+2^2+1.5*2*\sqrt{\smash[b]{2}})\approx

925210.49264925^2*10.49264

Total displacement is


925210.49264=92510.49264\sqrt{\smash[b]{925^2*10.49264}}=925*\sqrt{\smash[b]{10.49264}}\approx

9253.239=2996.075925*3.239=2996.075

Answer: 2996.075 km.


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