Athena W.

asked • 10/04/16# Problem solving- Complex Numbers and Roots

At a carnival, A new attraction allows contestants to jump off a springboard onto a platform to be launched vertically into the air. The object is to ring a bell located 20 feet overhead. The distance d(t)=16t^2-bt+20, where t is the time in seconds after leaving the platform, and b is the takeoff velocity from the platform.

1. Kate watches some of the contestants. She theorizes that if the platform lanches a contestant with a takeoff velocity of at least 32 ft./s the contestant can ring the bell.

a. Find the zeros for the function using 32 feet per second as the takeoff velocity.

B. Is Kate's theory valid?

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## 1 Expert Answer

Arturo O. answered • 10/04/16

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d(t) = (1/2)at

^{2}+ v

_{0}t + d

_{0}

a = -g = -32 ft/s

^{2}

v

_{0}= initial vertical velocity imparted by the platform, v

_{0}positive up

d

_{0}= height of platform (assume it is zero?)

Then

d(t) = -16t

^{2}+ v

_{0}t

Assume v

_{0}= 32 ft/s, and you want to reach a height of 20 ft. Is there a time t when this is realized?

20 = -16t

^{2}+ 32t

-16t

^{2}+ 32t - 20 = 0

Multiply both sides by -1 and get

16t

^{2}- 32t + 20 = 0

Divide by 4 to simplify a little.

4t

^{2}- 8t + 5 = 0

t = [8 ± √(64 - 4*4*5)] / 8

Note you get a complex number, so a launch speed of 32 ft/s will not get you up to 20 ft.

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Arturo O.

^{2}+ bt + 2010/04/16