Page 146 - How To Solve Word Problems In Calculus

on the wall. How fast is the beam moving when it is closest to
the police car?

Solution

x
θ
P
20

dθ
Given: = 2π (Since 1 revolution is 2π radians, the value of
dt
dθ
= 2π rad/sec.)
dt
dx
Find: when θ = 0 (The beam is closest to the police car
dt
when θ = 0.)

x
tan θ =
20
x = 20 tan θ

dx 2 dθ
= 20 sec θ ·
dt dt

dθ dx
Substituting θ = 0 and = 2π we compute :
dt dt
dx
2
= 20 · 1 · 2π = 40π ft/sec.
dt
EXAMPLE 4
A runner and his trainer are standing together on a circular
track of radius 100 meters. When the trainer gives a signal,
the runner starts to run around the track at a speed of 10 m/s.
How fast is the distance between the runner and the trainer
1
increasing when the runner has run of the way around the
4
track?

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