When will the softball hit the ground?

Question

The height of a softball is given by f(t)=−16t^2+83t+5.2 where f(t) represents the height of the softball in feet, and t is the number of seconds that has elapsed. Round all values to three decimal places.

1.When will the softball hit the ground? ____seconds

2.When will the softball be 20 feet above the ground? Write your answers as a list, with your answers separated by (a) comma(s). ____seconds

Answer 1

(1)

-16t² + 83t + 5.2 = 0

Solve for t, keep only the positive solution, and get

t = 5.249 sec

(2)

-16t² + 83t + 5.2 = 20

-16t² + 83t - 14.8 = 0

Solve for t and get

t = 0.185 sec (on the way up)
t = 5.003 sec (on the way down)

Answer 2

f(t)=−16t^2+83t+5.2

 

1.When will the softball hit the ground?

−16t^2+83t+5.2 = 0

 

after solving this quadratic equation using quadratic formula

t=-0.0619  and t =5.249

 

so softball will hit the ground after 5.249 seconds

 

 

2.When will the softball be 20 feet above the ground?

 

−16t^2+83t+5.2 = 60

after solving this quadratic equation by quadratic formula

t=0.776 and t =4.411

So softball be 20 feet above ground at 0.776 seconds and while returning to ground it be 20 ft above at 4.411 seconds

Answer 3

f(t)=−16t²+83t+5.2

When t=0, height is 5.2. The ball goes up t=83/32 (maximum point), then moves downward. It hits the ground when f(t)=0, that is

−16t²+83t+5.2=0. This happens when t=5.25

The same when f(t)=20 (above the ground)

−16t2+83t+5.2=20

Since the ball goes up and reaches the maximum height, 112.841 at t=83/32=2.60 (and then goes down), there are two points when it is 20 feet above the ground: t=0.25 and t=4.95.