Fireworks are being shot off of a 53.9 meter high roof of a building with a velocity of 49 meters per second.

Question

When will the embers of the firework reach the ground? When will the fireworks reach a maximum height, and what will the maximum height be?

Answer 1

The equation of motion is s(t) = -16t² + 49t +53.9.

If there is anything solid left of the material (embers will float and there is no way to predict when they will hit ground), it will hit ground when s(t)=0,

Maximum height will be attained when 32t=49.

This is true because the maximum height of a parabola will occur when t=-b/2a where

the parabola is given by ax²+bx+c=f(x). In order to show this by algebra you need to convert the equation to vertex form.