Question

during a baseball game, a player's ball hit into the outfield is modeled by the equation h=-16t^2 + 65t. A bird flying across the field follows the path modeled by the equation h=8t+20. let t be the time since the ball is hit and h be the height. what do the intersection points of the equations represent?

Answer 1

The intersections of the equations represent the times when the bird and the ball are at the same height.

8t+20=-16t^2+65t

16t^2-57t+20=0, using the quadratic equation for expediency:

t=(57±√4529)/32 and since we know t>0

t≈3.88 seconds (at a approximate height of 51 feet)

Answer 2

Intersection points are

(0.39,0) and (3.16,0)

Explanation:

The equation of the outfield is
`h=-16t^2 + 65t`

The path equation is
`h=8t+20`

To find intersection of two equations , we make them equal and solve for t

`-16t^2+65t= 8t+20`

Subtract 8t from both sides

`-16t^2+57t=20`

Subtract 20 on both sides

`-16t^2+57t-20=0`

Divide whole equation by -1

`16t^2-57t+20=0`

Apply quadratic formula to solve for t

`t=(-b+-√(b^2-4ac))/(2a)`

a= 16, b=-57 and c=20

`t=(57+-√((-57)^2-4(16)(20)))/(2(16))`

`t=(57+-√(1969))/(32)`

`t=(57+√(1969))/(32)=3.16`

`t=(57-√(1969))/(32)=0.39`