Question

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

Answer 1

Find derivative of h(t)

`\\ \rm\longmapsto (d)/(dx)(-16t^2+640t)`

`\boxed{\sf (d(x^n))/(dx)=nx^(n-1)}`

`\\ \rm\longmapsto -32t+640`

• Now its be 0

`\\ \rm\longmapsto -32t+640=0`

`\\ \rm\longmapsto -32t=-640`

`\\ \rm\longmapsto t=(-640)/(-32)`

`\\ \rm\longmapsto t=20s`

Answer 2

20 seconds

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