Question

An aeroplane flying at certain height declines at an angle of 30° and went straight
towards ground and to land at an airport. The average speed of aeroplane is 200
km/hr. It takes 54 seconds to reach the ground. How high was the aeroplane before
it started to descend.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Height=19.44\:km}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green {\underline \bold{Given : }} \\ \implies \text{Angle \: of \: elevation }= 30 \degree \\ \\ \implies \text{Avg. \: speed \: of \: aeroplane = 200 \: kmh} \\ \\ \implies \text{Time \: taken = 54 \: seconds} \\ \\ \red {\underline \bold{To \: Find : }} \\ \implies \text{Height \: at \: which \: aeroplane \: started \: desend = ?}$

• In the given question information given about a an aeroplane flying at certain height declines at an angle of 30° and went straight towards ground and to land at an airport. The average speed of aeroplane is 200 km/hr. It takes 54 seconds to reach the ground and we have to find How high was the aeroplane before it started to descend.

• According to given question :

$\text{Distance \: travelled \: by \: aeroplane} \\ \\ \implies Distance = speed \times time \\ \\ \implies D = 200 \times \frac{18}{5} \times 54 \\ \\ \implies D = 720 \times 54 \\ \\ {\green{\implies{\text{D = 38880 m = 38.88 km}}}} \\ \\ \text{In \: Right \: angle } \triangle \text{ABC} \\ \implies sin \: 30 \degree = \frac{p}{h} \\ \\ \implies \frac{1}{2} = \frac{p}{38.88} \\ \\ \implies p = \frac{38.88}{2} \\ \\ \green{\implies \text{p = 19.44 \: km}} \\ \\ \green{\therefore \text{Height \: at \: which \: aeroplane \: start \: descend \: is \: 19.44 \: km}}$

Answer 2

${distance \: travelled \: by \: aeroplane} \\ \\ \implies distance = speed \times time \\ \\ \implies d = 200 \times \frac{18}{5} \times 54 \\ \\ \implies d = 720 \times 54 \\ \\ {\green{\implies{d = 38880 m = 38.88 km}}}} \\ \\ \text{in \: right \: angle } \triangle \text{ abc} \\ \implies sin \: 30 \degree = \frac{p}{h} \\ \\ \implies \frac{1}{2} = \frac{p}{38.88} \\ \\ \implies p = \frac{38.88}{2} \\ \\ \green{\implies {p = 19.44 \: km}} \\ \\ \green{\therefore \text{height \: at \: which \: aeroplane \: start \: descend \: is \: 19.44 \: km}}$