# Thread: how fast distance is changing

1. ## how fast distance is changing

A plane flies directly over an observation point. The plane has constant altitude of 5000 ft. How fast is the distance between the plane and the point changing, at the instant the plane is 600ft past the overhead position and the plane is traveling 300 ft miles per hour?

NOTE: 5000ft=0.947 mile, and 600ft=0.1136 mile

2. Use Pythagoras.

$D^{2}=x^{2}+y^{2}$

Differentiate wrt time.

$D\cdot\frac{dD}{dt}=x\cdot\frac{dx}{dt}+y\cdot\fra c{dy}{dt}$

Let D be the hypoteneuse formed by the triangle we get.

You can find D by just using Pythagoras right out given x=600 and y=5000.

Remember, consistent units. That is the trick here. Be careful.

Fortunately, you're given the conversions.

Also y is constant, so dy/dt=0

You have all the knowns. Enter them in and solve for dD/dt

3. i am still a little confused....can you help me set this up a little further? im not sure where 300 mph comes in

4. 300 is dx/dt. That is the rate of the plane flying horizontally. The rate of change of x.