You’re flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 285 km south and 171 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?
here i will solve it thinking of it on a graph, with the y as a north/south axis and the x axis as east/west.
JBLM is at (285,0) and the destination is at (0,171)
your flight is the direct line from (285,0) to (0,171)
where is your flight, this line, closest to Mt. Rainier?
well the mountain is 56 km east of JBLM, so its x-value is 56
and it is 40 km south of JBLM, so 285-40=245
so Mt. Rainier is at (56, 245)
you will be closest to the mountain when the line tangent to your path that goes through (56,245) intersects your path
the line tangent to your path that goes through (56,245) has a slope of
the distance between your original point (0,285) and this point which is about 63 km. at 800km/hr, you will reach this point after .07875 hours or 4.725 min