Harriet jumped off a cliff into the ocean while vacationing with some friends

Question

Harriet jumped off a cliff into the ocean while vacationing with some friends. Her height above the ocean in feet, hh, as a function of time in seconds, t, is given by the function

h=−16(t^2−t−30)

How long will it take her to hit the water?

Answer 1

Solve this equation for t.

 

t² - t - 30 = 0

Answer 2

She hits the water when h(t) = 0.  Set h(t) = 0, which gives you a quadratic equation in t, and then solve for t.

 

-16(t² - t - 30) = 0

 

t² - t - 30 = 0

 

(t - 6)(t + 5) = 0

 

t = 6 or -5, but we cannot have negative time, since t = 0 starts at the moment she jumps.  Then

 

t = 6 seconds

Answer 3

Since h represents Harriet's height above the ocean in feet, if we are trying to find when Harriet will hit the water, that means we are trying to find when the value of h is 0, because Harriet's height above the water is 0 feet when she is hitting the water.  When given a quadratic equation, we can try to find when h is 0 by either factoring or using the quadratic equation.  Here if we look at the right side of the equation, -16(t^2-t-30), we can try to factor what is inside the parenthesis by starting with trying to find two numbers that will multiple to -30 and add up to -1. These two values are -6 and 5.  This means we can re-write the right side of the equation as -16(t-6)(t+5).  Since we want to know the values of t when h=0, we are trying to solve for t when 0=-16(t-6)(t+5).  By the zero product property (If two numbers multiply to zero, one of them must be zero) we know that we can set (t-6)=0 (and get t=6) and (t-5)=0 (and get t=-5).  This means that when t=6 and when t=-5, Harriet's height above the water would be 0.  Since we are talking about the time elapsed since she jumped off the cliff, here we would only need the positive value, so t=6.