How would you solve this problem using the quadratic formula???
1. Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t^2 + 16t + 480, where t is the time in seconds and h is the height in feet.
a. How long did it take for Jason to reach his maximum height?
b. What was the highest point that Jason reached?
c. Jason hit the water after how many seconds?
Thanks!
1. Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t^2 + 16t + 480, where t is the time in seconds and h is the height in feet.
a. How long did it take for Jason to reach his maximum height?
b. What was the highest point that Jason reached?
c. Jason hit the water after how many seconds?
Thanks!
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max height when -32t + 16 = 0 (the maximum is when the derivative (h'(t)) of h(t) = 0)
==> t = 1/2 seconds
(this can be done without the derivative, but it's a lot messier)
highest point: substitute t = 1/2 into h(t)
==> h(1/2) = -16/4 + 8 + 480 = 484 feet
he hits the water when h(t) = 0
so:
-16t^2 + 16t + 480 = 0
==> 16t^2 -16t - 480 = 0
==> t^2 - t - 30 = 0
==> (t -6)(t + 5) = 0
==> t = 6 seconds or t = -5 seconds, which can be ignored, because it's before he jumped)
==> t = 1/2 seconds
(this can be done without the derivative, but it's a lot messier)
highest point: substitute t = 1/2 into h(t)
==> h(1/2) = -16/4 + 8 + 480 = 484 feet
he hits the water when h(t) = 0
so:
-16t^2 + 16t + 480 = 0
==> 16t^2 -16t - 480 = 0
==> t^2 - t - 30 = 0
==> (t -6)(t + 5) = 0
==> t = 6 seconds or t = -5 seconds, which can be ignored, because it's before he jumped)