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?

Question

3091 views around the world

You can reuse this answer
Creative Commons License

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#