An aeroplane flying horizontally 750m above the ground lo an elevation of 60° . After 5 second the elevation is observed 30° . What is the speed of the aeroplane in km per hour?

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Answer 1 · 2018-08-09T15:13:00

The speed is $= 623.5 k m h^{- 1}$ $=623.5kmh^-1$

Let the speed of the plane $= v k m h^{- 1}$ $=vkmh^-1$

Then,

The distance travelled in $5 s$ $5s$ is

$d = \frac{v}{3.6} \cdot 5 = \frac{v}{0.72} = 1.389 m$ $d=v/3.6*5=v/0.72=1.389m$

Let the horizontal distance between the observer and the plane (first observation) be $= x m$ $=xm$

Then,

$tan 60 = \frac{750}{x}$ $tan60=750/x$ ................................ $(1)$ $(1)$

$tan 30 = \frac{750}{x + \frac{v}{0.72}}$ $tan30=750/(x+v/0.72)$ ................... $(2)$ $(2)$

Eliminationg $x$ $x$ from equations $(1)$ $(1)$ and $(2)$ $(2)$

$x = \frac{750}{tan 60} = 430.01$ $x=750/tan60=430.01$

$x + \frac{v}{0.72} = \frac{750}{tan 30} = 1299.04$ $x+v/0.72=750/tan30=1299.04$

$\frac{v}{0.72} = 1299.04 - 430.01 = 866.03$ $v/0.72=1299.04-430.01=866.03$

$v = 866.03 \cdot 0.72 = 623.5 k m h^{- 1}$ $v=866.03*0.72=623.5kmh^-1$