Question

A player kicks a soccer ball resting on the ground. The height of the ball, h(t), in feet, after t seconds can be represented by the function h(t) =−16t^2+96t. Use this information to answer the two questions that follow:

Part A: What is the total elapsed time, in seconds, from the time the ball is kicked until it reaches ground level again? ____ seconds

Part B: When will the ball reach its maximum height? After _____ seconds.

Answer 1

The correct answer is:

Part A: 6 Seconds

Part B: 3 Seconds

Explanation:

The given equation is:

⇒
`h(t) =-16t^2+96t`

Part A:

When h(t) = 0,

⇒
`-16t^2+96t=0`

On taking "t" as common, we get

⇒
`t(-16t+96)=0`

⇒
`-16t+96=0`

On adding "16t" both sides, we get

⇒
`-16t+96+16t=0+16t`

⇒
`96=16t`

⇒
`t=(96)/(16)`

⇒
`t=6 \ Seconds`

Part B:

When
`(dh(t))/(dt) =0`

⇒
`(d)/(dt)(-16t^2+96t)=0`

⇒
`-32t+96=0`

On adding "32t" both sides, we get

⇒
`-32t+96+32t=0+32t`

⇒
`96=32t`

⇒
`t=(96)/(32)`

⇒
`t=3 \ Seconds`