Casie jumped off of a cliff into the ocean while on vacation. Her height as a function of time is modeled by the equation h = −1
6t2 +16t + 140, where t is the time in seconds and h is the height in feet. How long does it take Casie to hit the water? A) 3 seconds
B) 3.5 seconds
C) 4 seconds
D) 4.5 seconds
This is an upside down parabola, a function that is extremetly useful in helping us to understand position and velocity and time and how they are all related. Her upwards velocity is 16 ft/sec and she starts from a height of 140 feet, according to the problem. The h is the height she ends up at after a certain amount of time has gone by. You want to know how long it will take her to hit the water. When she hits the water, she has no more height. Therefore, her height above the water when she hits the water is 0. Plug in a 0 for h and factor the quadratic to get t = -2.5 seconds and t = 3.5 seconds. The only two things in math that will never ever be negative is a distance measure and time, so we can disregard the -2.5 and go with 3.5 seconds as our answer.
