Thursday

September 18, 2014

September 18, 2014

Posted by **jason** on Monday, March 16, 2009 at 2:32am.

plane flying horizontally due north at a fixed altitude of

4 miles passes directly over the train. When the train has

traveled another mile, it is going 80 mph, and the plane

has traveled another 5 miles and is going 500 mph. At

that moment, how fast is the distance between the train

and the plane increasing?

- calculus -
**drwls**, Monday, March 16, 2009 at 5:06amLet's measure position from the ground location at noon, where the train was when the plane was overhead. It will make the math simpler but will not affect the answer. North position from there will have a "j" unit vector and west poeitiom from there will have a "-i" unit vector. The vertical unit vector is k.

At the time in question, the airplane position vector is

R2 = (5 + 500 t) j + 4 k

and the train position vector is

R1 = -(1 + 80 t)i

The separation vector is

D = R2 - R1 = (1 + 80 t)i + (5 + 500 t) j + 4 k

The rate of change of this vector is

dD/dt = 80 i + 500j mph

Take the square root of the sum of the squares for the rate the distance in increasing.

That would be 506.4 mph

Note that the altitude and the separation at that time do not matter, only the speeds.

**Answer this Question**

**Related Questions**

Calculus - A train is heading due west from St. Louis. At noon, a plane flying ...

Calculus - A train is heading due west from St. Louis. At noon, a plane flying ...

college - A train is heading due west from St. Louis. At noon, a plane flying ...

Math Calculus 2 - At a certain instant an aircraft flying due east at 240 miles ...

Math - a plane flies due north at 300 mi/h for 3 h then due west at 250 mi/h. If...

calculus - a plane flying horizontally at an altitude of 2 mi and a speed of 460...

physics - You are on an airplane traveling 30° south of due west at 130.0 m/s ...

calculus - An airplane flying west at 300 miles per hour goes over the control ...

calculus - A plane flying horizontally at an altitude of 1 mi and a speed of 560...

calculus 1 - I just need help getting started. I can't figure out the equation I...