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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.

Sagot :

Cricetus

Answer:

The correct answer is:

Part A: 6 Seconds

Part B: 3 Seconds

Step-by-step explanation:

The given equation is:

⇒  [tex]h(t) =-16t^2+96t[/tex]

Part A:

When h(t) = 0,

⇒ [tex]-16t^2+96t=0[/tex]

On taking "t" as common, we get

⇒ [tex]t(-16t+96)=0[/tex]

⇒ [tex]-16t+96=0[/tex]

On adding "16t" both sides, we get

⇒ [tex]-16t+96+16t=0+16t[/tex]

⇒                      [tex]96=16t[/tex]

⇒                        [tex]t=\frac{96}{16}[/tex]

⇒                        [tex]t=6 \ Seconds[/tex]

Part B:

When [tex]\frac{dh(t)}{dt} =0[/tex]

⇒ [tex]\frac{d}{dt}(-16t^2+96t)=0[/tex]

⇒          [tex]-32t+96=0[/tex]

On adding "32t" both sides, we get

⇒ [tex]-32t+96+32t=0+32t[/tex]        

⇒                      [tex]96=32t[/tex]

⇒                        [tex]t=\frac{96}{32}[/tex]

⇒                        [tex]t=3 \ Seconds[/tex]

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