Question

This is a question regarding quadratic equations. I think I have to use the quadratic formula but I'm not sure and because the question provides the base I think I'm wrong. Here is the question|:

During a hurricane, parabolic waves on the ocean can exceed a height of 30 m above sea level. A ship hits a wave that rises 30 m above sea level and is 40 m wide at its base. If the wave hits the ship at 10 m/s, for how long will the ship be greater than 10 m above sea level?

Answer 1

if we set the wave with its vertex at (0,30) and it has height 0 at x=-20 and 20.

y = 30-ax^2
y(20) = 0, so 30/400 = a = 0.075
y = 30 - .075x^2

Now we want to know where y > 10:

30 - .075x^2 > 10
20 > .075x^2
-16.32 < x < 16.32
So, to travel a distance of 32.64m at 10 m/s requires 3.264 seconds.

See

http://www.wolframalpha.com/input/?i=plot+y%3D30+-+.075x%5E2%2C+y%3D10