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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]