Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. assume the starting height of the ball is 0 feet. approximately how long does it take until the soccer ball hits the ground again?
1.3 secs
2.6 secs
16.0 secs
27.6 secs

A=g

v=⌠g dt

v=gt+C, where C=v initial

v=gt+vi

h=⌠v dt

h=gt^2/2+vit+C, where C=h initial

h=gt^2/2+vit+hi

We are told that vi=42 ft/s, hi=0, and we know g≈-32 ft/s^2 so

h(t)=-16t^2+42t

The ball will hit the ground when h=0 so

-16t^2+42t=0

-2t(8t-21)=0, since t>0

8t-21=0

8t=21

t=21/8

t=2.625 sec

t≈2.6 sec (to nearest tenth of a second)