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 $=623.5kmh^-1$

Let the speed of the plane $=vkmh^-1$

Then,

The distance travelled in $5s$ is

$d=v/3.6*5=v/0.72=1.389m$

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

Then,

$tan60=750/x$ ................................ $(1)$

$tan30=750/(x+v/0.72)$ ................... $(2)$

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

$x=750/tan60=430.01$

$x+v/0.72=750/tan30=1299.04$

$v/0.72=1299.04-430.01=866.03$

$v=866.03*0.72=623.5kmh^-1$