Answer:
DL/dt = 529 miles/h
Step-by-step explanation:
The radio station (point A) the point just up the radio station ( point B), and the variable position of the plane ( at specif t point C) shape a right triangle wich hypothenuse L is:
L² = d² + x²
d is the constant distance between the plane and the ground
Then differentiation with respect to time on both sides of the equation
2*L*dL/dt = 2*d* Dd/dt + 2*x*dx/dt
But Dd/dt = 0
L*dL/dt = x*dx/dt
x = 5 miles dx/dt = 570 m/h L = √ d² + x² L √ (5)² + (2)²
L = √29 L = 5.39 m
5.39 *DL/dt = 5*570 m/h
DL/dt = 5*570/5.39 miles/h
DL/dt = 528.76 miles/h
DL/dt = 529 miles/h
