Question

H=-16t^2+122t+5 where h is height in feet and t is time in seconds. How long will it take the baseball to hit the ground? h=-16t^2+162t+0.2 where h is height in feet and t is time in seconds. How long will it take the golf ball to hit the ground?

Answer 1

`t= 7.67`

`t= 10.13s`

Explanation:

Solving (a):

`H=-16t^2+122t+5`

Required: Time to hit the ground

This means that H = 0

So, we have:

`0=-16t^2+122t+5`

Rewrite as:

`16t^2-122t-5=0`

Solve for t using:

`t= (-b \± √(b^2 - 4ac))/(2a)`

`t= (122 \± √((-122)^2 - 4*16*-5))/(2*16)`

`t= (122 \± √(15204))/(2*16)`

`t= (122 \± 123.3)/(32)`

Split:

`t= (122 + 123.3)/(32)` or
`t= (122 - 123.3)/(32)`

`t= (245.3)/(32)` or
`t= (-1.3)/(32)`

`t= 7.67` or
`t= -0.0406`

Time can not be negative. so:
`t= 7.67`

Solving (b):

`h=-16t^2+162t+0.2`

Required: Time to hit the ground

This means that h = 0

`0=-16t^2+162t+0.2`

Rewrite as:

`16t^2-162t-0.2= 0`

Solve for t using:

`t= (-b \± √(b^2 - 4ac))/(2a)`

`t= (162 \± √((-162)^2 - 4*16*-0.2))/(2*16)`

`t= (162 \± √(26256.8))/(32)`

`t= (162 \± 162.04)/(32)`

`t= (162 + 162.04)/(32)` or
`t= (162 - 162.04)/(32)`

`t= (324.04)/(32)` or
`t= (-0.04)/(32)`

Time can not be negative. So:

`t= (324.04)/(32)`

`t= 10.13s`