On a vacation in Puerto Rico rose jumped off a cliff into a river in El Yunque go forest reserve her height as a function of time could be modeled by the function h(t) = -16 = -16t^2 + 16t + 480, where T is the time after jumping in seconds and H is the height in feet how many seconds did it take Rose to hit the water

Question

On a vacation in Puerto Rico rose jumped off a cliff into a river in El Yunque go forest reserve her height as a function of time could be modeled by the function h(t) = -16 = -16t^2 + 16t + 480, where T is the time after jumping in seconds and H is the height in feet how many seconds did it take Rose to hit the water

Answer 1

To find out how many seconds it took for Rose to hit the water, we need to find the time when her height is equal to 0 (i.e., when she hits the water).

So, we need to solve the equation -16t^2 + 16t + 480 = 0 for t.

First, let's rewrite the equation:
-16t^2 + 16t + 480 = 0

Now, we can use the quadratic formula to solve for t:
t = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = -16, b = 16, and c = 480. Plugging these values into the formula, we get:
t = (-16 ± √(16^2 - 4*(-16)*480)) / (2*(-16))
t = (-16 ± √(256 + 30720)) / -32
t = (-16 ± √(30976)) / -32
t = (-16 ± 176) / -32

So, the two possible solutions are:
t = (-16 + 176) / -32 = 160 / -32 = -5
t = (-16 - 176) / -32 = -192 / -32 = 6

Since time cannot be negative, the only valid solution for t is 6 seconds. Therefore, it took Rose 6 seconds to hit the water after jumping off the cliff.