Question

An arrow is shot upward. Its height h, in feet, is given b the equation h=-16t^2+32+5, where t is the time in seconds. How many seconds does it take until the arrow hits the ground?

Answer 1

is h the height or the feet ?

Answer 2

The time taken to reach the ground is t=2.146 approx 2 seconds.

Explanation:

Given : An arrow is shot upward. Its height h, in feet, is given by the equation
`h(t)=-16t^2+32t+5`, where t is the time in seconds.

To find : How many seconds does it take until the arrow hits the ground?

Solution :

We have given the equation,
`h(t)=-16t^2+32t+5`

where, h is the height in feet and t is the time in seconds.

We have to find in how many seconds does it take until the arrow hits the ground i.e. height became zero or h(t)=0

Substituting in the equation,

`0=-16t^2+32t+5`

Solve by quadratic formula,

Solution of equation
`ax^2+bx+c=0` is
`x=(-b\pm√(b^2-4ac))/(2a)`

On comparing, a=-16 , b=32 , c=5

Solution is

`t=(-32\pm√((32)^2-4(-16)(5)))/(2(-16))`

`t=(-32\pm√(1024+320))/(-32)`

`t=(-32\pm√(1344))/(-32)`

`t=(-32\pm 36.66)/(-32)`

`t=(-32+36.66)/(-32),(-32-36.66)/(-32)`

`t=-0.146,2.146`

We reject t=-0.146.

So, The time taken to reach the ground is t=2.146 approx 2 seconds.