Question

David kicks a soccer ball off the ground and in the air with an initial velocity of 35 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches?

17.9 feet

18.2 feet

18.7 feet

19.1 feet

Answer 1

are you allowed to use calculus? or is this strictly algebra?

Answer 2

It doesn't say... So i'm guessing i can use whatever @lgbasallote

Answer 3

algebraically- find the vertex x=b/2a then find y
or find the derivative, set it equal to 0 and solve for x, then solve for y

Answer 4

I got 18.2 feet, at first... @completeidiot

Answer 5

ok s = 0 because he's kicking the ball from the ground
so H(t)= -16 t^2+35t
so solving using derivative
0=-32t+35
t= 1.09375
so H(1.09375) =?

Answer 6

algebraically
t= -b/(2a)
t= 1.09375
so H(1.09375)= ?

Answer 7

Okay.. and?

Answer 8

I'm still kind of confused sorry

Answer 9

ok solving it using derivatives,
basically what you're given is the height equation, at any given moment t, the ball will be at H height and it would look something like this


so the highest point would be at the vertex of this parabola which can be found by t=-b/(2a)
once you have the time, you can substitute this value back into the equation you were given to find the maximum height at that time

if you look at it using derivatives, the derivative of the height equation would be the velocity equation, so when the ball reaches its maximum height, its velocity would be equal to 0, which is why we set the derivative equal to 0.
we solve for the time when velocity is 0, then use that time to determine the maximum height