*Question by geklein3*: How to solve vertical motion equations?

the problem is:

Cliff diving. A cliff diver jumps from a ledge 96 feet above the ocean with an initial upward velocity of 16 feet per second. How long will it take until the diver enters the water? Use the equation h=-16t^2+vt+s, where v+ initial vertical velocity and h+ initial hight.

Thanks for the help!

**Best answer:**

*Answer by mathgirl*

I think you have your variables a little confused. If you are using the equation:

h = -16t^2 +vt + s

then

h = height of the diver (in feet) at time t (in seconds)

t = time (in seconds)

v = initial vertical velocity (in ft/s)

s = initial height (in feet)

So, you are given the following information,

v = 16 ft/s

s = 96 ft

Put the information you are given into the equation and you get:

h = -16t^2 + 16t + 96

You are asked to find the time (t) when the diver enters the water (when h = 0 ft). So, set h=0 and solve for t:

0 = -16t^2 + 16t + 96 … divide both sides by -16

0 = t^2 – t – 6 … either use quadratic formula or factor to solve

0 = (t – 3)(t + 2)

t = 3 or -2

Since we are looking for the time it took to reach the water, we can logically throw out the negative number, and we get an answer of 3 seconds.

Hope that helps!

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