Plane cruising speed

Question

An airplane is cruising at an altitude of 10 000 m. It is flying in a straight line away from chandra, who is standing on the ground. If she sees the angle of elevation of the airplane change from 70 degrees to 30 degrees in 1 minute. What is the cruising speed to the nearest kilometer per hour

Answer 1

The cruising speed, s, during that 1 minute is going to be 

 

s=distance traveled/time

 

the distance traveled you can figure out from the angles and cruising altitude using the tangent function

When the plane is at 70 degrees from where Chandra is standing, it is at a distance d_i=10km/tan(70°)=3.6km away.

When the plane is at 30° from where Chandra is standing, it still has the same cruising altitude (height) and is just further away, so it is now at a distance d_f=10km/tan(30°)=17km away.

 

s=((17-3.6)km/1min)*60min/hr= 820km/hr

 

I multiplied by 60 min/hr to convert the speed from km/min to km/hr