Page 65 - How To Solve Word Problems In Calculus

EXAMPLE 6
A plane, P, flies horizontally at an altitude of 2 miles with a
speed of 480 mi/h. At a certain moment it passes directly over
a radar station, R. How fast is the distance between the plane
and the radar station increasing 1 minute later?

Solution
Step1

x P

2 z

R

Step2
dx
Given: = 480
dt

dz
Find: 1/60 hour later ← Units of time must be consistent
dt throughout the problem

Step3
2
2
2
By the theorem of Pythagoras, z = x + 2 .
Step4
dz dx
2z = 2x + 0
dt dt

dz dx
z = x
dt dt

Step5
Since the plane travels 480 mi/h, it will have flown 8 miles

1 1
in hour 480 × = 8 . Since x = 8, the value of z is easily
60 60
determined by the Pythagorean theorem.
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