Question

The height in feet above the water of a diver can be modeled by ℎ() = −16*2 − 16 + 192, where t is the time in seconds after the diver jumps off a platform. Find the time it takes for the diver to reach the water.

(Solve using any method you wish.)

Answer 1

h(t) is the height of the diver in feet above the water

Now it asks about the time at which diver reaches the water

When diver reaches the water , the height of diver from water should be zero

So we plug h(t) =0

So

`-16t^2 -16 t +192 =0`

divide whole equation by -16

`t^2 +t -12 =0`

we can now factor the quadratic equation

So we get

(t+4)(t-3) =0

plug each factor equal to zero and solve for t

t+4 =0 and t-3 =0

So t=-4 and t=3

Now time cannot be negative , So t=3

So time = 3 seconds

It takes 3 seconds for the diver to reach the water