# 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?

Aug 9, 2018

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

#### Explanation:

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

Then,

The distance travelled in $5 s$ is

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

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

Then,

$\tan 60 = \frac{750}{x}$................................$\left(1\right)$

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

Eliminationg $x$ from equations $\left(1\right)$ and $\left(2\right)$

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

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

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

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