Question

A ball is dropped from the top of a 550 ft. building. The function h(t) = - 16t2 + 50 models the height of the ball, h(t) (in feet), at any given time, t (in seconds).

What is the maximum height of the ball?


423 ft



550 ft

Answer 1

is h(t) -16t^2 + 550 instead of that 50?

Answer 2

its 50

Answer 3

It can't just be 50

Answer 4

the height function is decreasing faster and faster (acceleration)

the max is when t=0, should be th etop of the building at h(0)=550ft

Answer 5

the number on the end of h(t) is the initial height h(0), in this case, it is the same as the building height

Answer 6

I thought it was 423 ft , but i guessed and i really need to know how to do these because i have a test with like 10 problems.

Answer 7

is this just math class with given functions and stuff, or you in physics doing kinematics

Answer 8

Its algrbra

Answer 9

time t, will be just positive, so the graph of h(t) is just the right half of an upside down parabola

Answer 10

the height starts at time t=0

h(0) = 50 vertex of the parabola, maximum value in this case

Answer 11

however, it says it was dropped from a height of 550, one thing is not right

Answer 12

but i dont know which to put ??

Answer 13

There may be a typo, but to make sense, the equation is probably
\[ h(t) = -16t^2 + 550\]
in this problem, they say the ball is dropped from the top of a building
(we would say at time t=0)
the ball then falls.

The highest the ball will be is at the start, at 550
it then falls

Answer 14

Right

Answer 15

if we did it just using math (and using the correct equation
h(t)= -16 t^2 + 0 t + 550
(I put in the missing "t" term)
and match that with
y= a t^2 + b t + c
we match a with -16
b with 0
c with 550

and we use the formula that the vertex (highest point of the parabola)
happens at
t= -b/(2a)

with b=0 and a= -16 we get
t= -0/(2*-16) = 0

the math says the highest point is at t=0
and the highest height will be
-16*0*0 +550 = 0+550= 550

Answer 16

Thank you so much

Answer 17

But why add 550 ?

Answer 18

I used the formula
\[ h(t)= -16t^2 + 550\]
instead of \( h(t)= -16t^2 +50\)
because the new equation "works" (I know the ball is 550 ft high (on top of the building)
and the second equation says the ball is at 50 feet high (at time t=0)
also, I know math problems sometimes have typos.

So I fixed the equation.