marsha threw her math book off a 30 foot building.The equation of the book can be represented by the equation h=-16t+24t+30

Answer 1

h = -16t² + 24t + 30

At time t=0, h=30

At time t=1, h= -16(1²) + 24(1) +30 = -16+24+30 = 38

At time t=2, h= -16(2²) + 24(2) + 30 = -16*4 + 48 + 30 = 14

At time t=3, h= -16(3²) + 24(3) + 30 = -16*9 + 72 + 30 = -144+102 = -42. <== clearly too far

So the book reaches the ground at a time between t=2 and t=3.

Let a = -16, b=24 and c=30

By the quadratic formula, h=0 when t = [-b +/- sqrt(b² - 4ac)] / 2a

Plugging values of a, b and c into the formula, t = [-24 +/- sqrt(2496) / -32

t = (-24+49.96) / -32 = -0.81 (not possible), OR

t = (-24-49.96) / -32 = 2.31 which is the correct answer. Note, as shown above, t is between 2 and 3.