33-34 Time Rates: A car traveling east and airplane traveling north

Problem 33
From a car traveling east at 40 miles per hour, an airplane traveling horizontally north at 100 miles per hour is visible 1 mile east, 2 miles south, and 2 miles up. Find when this two will be nearest together.
 

Problem 34
In Problem 33, find how fast the two will be separating after along time.
 

31-32 Train in an elevated track and car in perpendicular road

Problem 31
An elevated train on a track 30 ft above the ground crosses a street at the rate of 20 ft/sec at the instant that a car, approaching at the rate of 30 ft/sec, is 40 ft up the street. Find how fast the train and the car separating 1 second later.
 

Problem 32
In Problem 31, find when the train and the car are nearest together.
 

22-24 One car from a city starts north, another car from nearby city starts east

Problem 22
One city C, is 30 miles north and 35 miles east from another city, D. At noon, a car starts north from C at 40 miles per hour, at 12:10 PM, another car starts east from D at 60 miles per hour. Find when the cars will be nearest together.
 

Problem 23
For the condition of Problem 22, draw the appropriate figure for times before 12:45 PM and after that time. Show that in terms of time after noon, the formulas for distance between the two cars (one formula associated with each figure) are equivalent.
 

19-21 Two cars driving in parallel roads

Problem 19
One city A, is 30 mi north and 55 mi east of another city, B. At noon, a car starts west from A at 40 mi/hr, at 12:10 PM, another car starts east from B at 60 mi/hr. Find, in two ways, when the cars will be nearest together.
 

Problem 20
For the condition of Problem 19, draw the appropriate figures for times before 12:39 PM and after that time. Show that in terms of time after noon, the formula for distance between the two cars (one formula associated with each figure) are equivalent.
 

Problem 21
For Problem 19, compute the time-rate of change of the distance between the cars at (a) 12:15 PM; (b) 12:30 PM; (c) 1:15 PM