Question

Jake tosses a coin up in the air and lets it fall to the ground. The equation that models the height (in feet) and time (in seconds) of the parabola is h(t)= -16t^2+ 24t+6. What is the height of the coin when Jake tosses it?

Answer 1

The maximum height of coin Jake tosses is 15 feet.

Explanation:

Given Jake tosses a coin up in the air

and the height of coin is model by h(t)=
`(-16)t^(2) +24t+6`

To find height of the coin when Jake tosses it:

When a coin is in the hand of Jake, time t=0

Height of coin is h(t)=
`(-16)t^(2) +24t+6`

h(0)=
`(-16)(0)^(2) +24(0)+6`

h(0)=6 feet.

Therefore, Height of coin at time t=0 is 6.

For maximum height of the coin,

h(t)=
`(-16)t^(2) +24t+6`

Differentiating both side,

`(d)/(dt)h(t)=(d)/(dt)[(-16)t^(2) +24t+6]`

`(d)/(dt)h(t)=(d)/(dt)[(-32)t+24]`

`(d)/(dt)h(t)=0`

`(d)/(dt)[(-32)t+24]=0`

t=
`(24)/(32)`

t=
`(3)/(4)`

t=0.75

Now,

h(t)=
`(-16)t^(2) +24t+6`

h(0.75)=
`(-16)(0.75)^(2) +24(0.75)+6`

h(0.75)=15 feet.

The maximum height of coin jake tosses is 15 feet.