Question

A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t^2 + 640t. After how many seconds does the projectile take to reach its maximum height? Show your work.

Answer 1

@phi

Answer 2

@Hero @mathstudent55

Answer 3

h(t) = - 16t^2 + 640t

if you write it as
\[ y = - 16x^2 + 640x \]
to make it look more familiar (?), that is the equation of a parabola, with a "frown" shape \( \cap \)
Its "peak" is at its vertex.

Do you remember how to find the x value of the vertex?
it is -b/(2a) when the equation is in the form
\[ y = a x^2 +bx + c\]

Answer 4

-640/-32?

Answer 5

yes, which is ?

Answer 6

20

Answer 7

yes. x=20. Or, going back to the original equation
\[ h(t) = - 16t^2 + 640t \]
t=20 seconds
that is how many seconds the projectile takes to reach its maximum height

Answer 8

they don't ask, but the height would be
h(20)= -16*20*20 + 640*20 = 6400

Answer 9

Thank you so much!

Answer 10

yw