Question

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)

Answer 1

Using law of cosines, square of total displacement is

$$(925*1.5)^2+(925*2)^2-\newline -2*(925*1.5)*(925*2)*cos(180-45)=$$

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

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

$$925^2*(1.5^2+2^2+1.5*2*\sqrt{\smash[b]{2}})\approx$$

$$925^2*10.49264$$

Total displacement is

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

$$925*3.239=2996.075$$

Answer: 2996.075 km.