Question

${\huge{\blue\dashrightarrow{\texttt{\orange Q\red U\green E\pink S\blue T\purple ION\red}}}}$

The angle of elevation of a plane from a point A on the ground is 60° . After a flight of 30 seconds the angle of elevation changes to 30° . If the plane is flying at a constant height of 3600√3m , find the speed of the plane .

No spam ! Spammers will be reported

Answer 1

question :-

The angle of elevation of a plane from a point A on the ground is 60° . After a flight of 30 seconds the angle of elevation changes to 30° . If the plane is flying at a constant height of 3600√3m , find the speed of the plane .

solution :-

→ tan 60° = AD/CD

→ CD = AD/ tan 60°

substituting AD = 3600√3 and tan 60 = 3 we get

→ CD = 3600√3/√3

→ CD = 3600

in triangle BCE at angle C we get

→ tan 30 = BE/CE

→ CE = BE/tan 30

→ CD + DE = BE / tan 30

substituting BE = 3600 √3 and tan 30 = 1/√3

CD = 3600 and DE = 30s we get

3600 + 30s = 3600√3/1/√3

→ 30s = (3600 × √3 × √3) - 3600

→ 30s = 3600 (3 - 1)

→ s = 120(2)

→ s = 240m/s

therefore the speed of the plane is 240m/s

$\:$

Answer 2

${\huge{\blue\dashrightarrow{\texttt{\orange Q\red U\green E\pink S\blue T\purple ION\red}}}}$

The angle of elevation of a plane from a point A on the ground is 60° . After a flight of 30 seconds the angle of elevation changes to 30° . If the plane is flying at a constant height of 3600√3m , find the speed of the plane .

${\huge{\blue\dashrightarrow{\texttt{\orange A\red N\green S\pink W\blue E\purple R\red}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \sf {\tan60 \degree =\frac{BE}{AB}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \cancel{{ \sqrt{3}}} = \frac{3600 \cancel {\sqrt{3} }}{AB}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf {AB = 3600m}$

$\: \: \: \: \: \: \: \: \: \: \: \: \sf {\tan30\degree =\frac{DC}{AC}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf { \frac{ \: \: \: 1}{ \sqrt{3} } =\frac{3600 \sqrt{3} }{AB + BC}}$

$\: \: \: \: \: \: \: \: \: \sf{AB + BC = 3600 \times 3}$

$\: \: \: \: \: \: \: \: \: \sf{3600 + BC = 10800}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{BC = 7200m}$

$\: \: \: \: \: \: \: \: \: \: \boxed {\green{ \sf{speed = \frac{distance}{time}}} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: {\sf{speed = \frac{ BC}{time} } }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf{speed = \frac{7200}{30}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \sf\blue{speed = 240m/s}$