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Pre-Calculus Homework Help: Vertical Free Fall Motion Modeling

Learn about free fall motion in Pre-Calculus, solve problems using equations, and maximize revenue through graphs. Book and calculator needed. Practice exercises included.

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Pre-Calculus Homework Help: Vertical Free Fall Motion Modeling

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  1. Today in Pre-Calculus • Go over homework • Notes: (need book and calculator) • Modeling • Homework

  2. Vertical Free Fall Motion The height s and vertical velocity v of an object in free fall are given by s(t) = -½ gt2 + v0t + s0 and v(t) = -gt + v0 Where t is time (in seconds), g≈32 ft/sec2 ≈9.8m/sec2 is the acceleration due to gravity, v0 is the initial vertical velocity of the object, and so is its initial height.

  3. Example Page 184: Number 61 • s0 = 83 ft; v0=92 ft/sec s(t) = -½ (32)t2 + 92t + 83 = -16t2 + 92t +83 So maximum height is 215.25 ft. • s(t) = 0 (use quadratic formula) 6.543 sec • v(t) = -32t + 92 v(6.543) = -32(6.543) + 92 = -117.371 ft/sec

  4. Example Number 59 a) Revenue = quantity price R(x) = (26,000 – 1,000x)(0.50 + 0.05x) = 13,000 +800x – 50x2 b) Graph it so you can see the max and x-intercept c) h = -800/(2-50) = 8 So Revenue is maximized when x = 8 Price: 0.50 + 0.05(8)= $0.90 Revenue : 13,000 + 800(8) – 50(8)2 = $16,200

  5. Homework • Pg. 184: 58, 62, 63

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