# Fighter

A military fighter flies at an altitude of 10 km. From the ground position, it was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.

Correct result:

v =  1179.726 km/h

#### Solution:

$α=23 \ ^\circ \ \\ β=27 \ ^\circ \ \\ h=10 \ km \rightarrow m=10 \cdot \ 1000 \ m=10000 \ m \ \\ t=12 \ \text{s} \ \\ \ \\ \tan α=h/x_{1} \ \\ \tan β=h/x_{2} \ \\ \ \\ x_{1}=h/ \tan α ^\circ =h/ \tan 23^\circ \ =10000/ \tan 23^\circ \ =10000/ 0.424475=23558.52366 \ \\ x_{2}=h/ \tan β ^\circ =h/ \tan 27^\circ \ =10000/ \tan 27^\circ \ =10000/ 0.509525=19626.10506 \ \\ \ \\ x=x_{1}-x_{2}=23558.5237-19626.1051 \doteq 3932.4186 \ \text{m} \ \\ \ \\ v_{1}=x/t=3932.4186/12 \doteq 327.7016 \ \text{m/s} \ \\ v=v_{1} \rightarrow km/h=v_{1} \cdot \ 3.6 \ km/h=327.701550258 \cdot \ 3.6 \ km/h=1179.726 \ km/h=1179.726 \ \text{km/h}$

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