Another question on word problems

Question

Jason jumped off of a cliff into the ocean. 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.

How long did it take for Jason to reach his max height?

What was the highest point that he reached?

Jason hit the water after how many seconds?

Answer 1

From the equation and description, we know that he jumped up---i.e. his initial velocity was up. The equation is in the form:

d = -at² / 2 + v_i * t + d_i , where a is the acceleration of gravity, v_i is the initial velocity, and d_i is the initial distance the height of the cliff.

So, the initial velocity is 16 ft/sec. a = 32 ft/sec² , so the time to get to zero velocity is v/a = 0.5 second.

To get the total time, simply set the equation = to zero and solve for t:

-16t² + 16t + 480 = 0

Simplify:

t² - t - 30 = 0 This is factorable, so the rest is easy. You'll get both + and - values for t. Only the + value is significant