Today in Pre-Calculus

• Go over homework• Notes: (need book and

calculator)– Modeling

• Homework

Vertical Free Fall MotionThe 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.

ExamplePage 184: Number 61

a) s0 = 83 ft; v0=92 ft/sec

s(t) = -½ (32)t2 + 92t + 83 = -16t2 + 92t +83

So maximum height is 215.25 ft.

b) s(t) = 0 (use quadratic formula)

6.543 sec

c) v(t) = -32t + 92

v(6.543) = -32(6.543) + 92 = -117.371 ft/sec

2922.875 16(2.875) 92(2.875) 83 215.25

2( 16)h k

ExampleNumber 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

Homework

• Pg. 184: 58, 62, 63