An explosion causes debris to rise vertically with an initial velocity of 160 feet per second.

Question

In how many seconds does it attain maximum height?

i know i need to use the formula:
y(t)=-16t^2+Vot + yo
Have:
vo=160
Yo= is what i am trying to find
and i dont know how to solve for time

Answer 1

so you know:
height = -16t^2 + 160t + 0 , zero, since we started at ground level

This is a downwards opening parabola, so it has a maximum at its vertex.
What method have you learned to find the vertex, there are several ways.

simplest way in this case:
find the x-intercepts, then find the midpoint

h = -16t^2 + 160t
= -16t(t - 10)
so the intercepts are 0 and 10,
then half-way time is 5 seconds