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A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t2 + 640t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit

Respuesta :

ferrybukantoro

Answer:

20 seconds

Step-by-step explanation:

h(t) = -16t2 + 640t

to find the maximum value =>

h'(t) = 0

-32t + 640 = 0

-32(t -20)= 0

t-20 = 0

t = 20 seconds

Find derivative of h(t)

[tex]\\ \rm\longmapsto \dfrac{d}{dx}(-16t^2+640t)[/tex]

[tex]\boxed{\sf \dfrac{d(x^n)}{dx}=nx^{n-1}}[/tex]

[tex]\\ \rm\longmapsto -32t+640[/tex]

  • Now its be 0

[tex]\\ \rm\longmapsto -32t+640=0[/tex]

[tex]\\ \rm\longmapsto -32t=-640[/tex]

[tex]\\ \rm\longmapsto t=\dfrac{-640}{-32}[/tex]

[tex]\\ \rm\longmapsto t=20s[/tex]

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