2'6 More Related Rates

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2.6 More Related Rates

• November 5

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Example 4

• A man (6 ft) walks away from a lamp post (15 ft)
  at 5 ft/sec. How fast is his shadow lengthening?
  How fast is the shadow's tip moving?

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Example 4

• Given dm/dt 5
• Find ds/dt and d(ms)/dt dm/dt ds/dt
• Eqn By ?s we know
• man's ht shadow length
• lamp's ht dist. lamp to shadow tip
• So 6/15 s/(ms) and
• S 2m/3 or m 3s/2

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Example 4

• S 2m/3
• Dif ds/dt 2/3 dm/dt
• So ds/dt 2/3 (5) 10/3 ft/sec
• d(ms)/dt dm/dt ds/dt 5 10/3
• 25/3 ft/sec

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Example 5

• A plane (alt. 4000 ft) is flying west at 700
  ft/s. A searchlight, under its path, tracks it.
• How fast is the light pivoting when the plane is
  1000 ft east, overhead, 5000 ft west?
• (see CiM)

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Example 5

• Given dx/dt -700
• Find d?/dt when x 1000
• Eqn tan? x/4000
• Dif sec2? d?/dt 1/4000 dx/dt
• Note when x 1000, tan? 1/4
• So ? tan-1(1/4) 0.245 radians

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Example 5

• sec2? d?/dt 1/4000 dx/dt
• sec2 (0.245) d?/dt 1/4000 (-700)
• d?/dt (-7/40)cos2(0.245)
• d?/dt -0.165 radians/sec

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Add to 17

• p. 146
• 21,22,24,25,28, 31,32,33,39,42
• (have 16 ready tomorrow)