Question

An air force plane is ascending vertically at the rate of 100 km/hr.if teh radius of the earth is r km how fast is the area of the earth visible from the plane

Answer 1

The change of height with time is :

dh/dt = 100

Area = (2πr²h) / (r + h)

We want to find the change in area with time as follows :

dA/dt = (dA / dh) × (dh/dt)

dA/dh = 2πr²d/dh (1/(r + h))

= 2πr²{( (r +h) - h ) / (r + h)²}

dA/dt = 2πr²{( (r + h) - h ) / (r + h)²} × 100

= 200πr³ / (r + h)²

This is the rate of change of visibility of the area of the earth.

Answer 2

HEY HERE IS YOUR ANSWER...

The change of height with time is:

dh/dt = 100

Area = (2pie squareh)/ (r+h)

We want to find the change in area with time as follows:

dA/dt = (dA/dh) × (dh/dt)

dA/dh = 2 pie rsquare d/dh (1/(r+h))

= 2pie rsquare {( (r+h)- h)/ (r+h)square}

dA/dt = 2pie rsquare {( (r+h)-h/ r+h)square} × 100

= 200pie r 3/(r+h)square.

This is the rate of change of visibility of the area of the earth.

Hope it Helps....