Looking for maximum height the ball will reach in feet. h(t)=16t^2+30t+6?

Question

h= height
t= seconds

The height, h, in feet, a ball will reach when thrown in the air is a function of time, t, in seconds, given by the equation
h(t)=-16t^2+30t+6. Find the maximum height the ball will reach.

Answer 1

Are you sure it's not -16t^2 + 30t +6?

16t^2+30t+6 is concave up, so it looks kind of like a U, therefore it increase without bound, therefore it does not have a maximum height. (in projectile motion equations, the a term is usually (1/2) gravity (-16ft/sec^2), and considered to be negative, b is the initial velocity, and h is the initial height). With that in mind:

-16t^2 +30t +6 is concave down, so it looks like n. It's maximum would be at the vertex, or when t= -b/2a

b = 30 a =-16

t = -30/-32
t = 15/16 seconds ~.9375 seconds

maximum would occur at 15/16 seconds. substituting into the equation you find the height at this time to be

321/16 ft ~ 20.0625 ft

Answer 2

There is no maximum height, as it will continue rising with time (and speeding up). For something to slow down over time, you need an element of the equation which is subtracting t.
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Taking into account additional details

The maximum occurs when the differential is 0 (i.e., if you plotted the graph, where the gradient is 0).

Differentiating -16t² + 30t + 6 gives -32t + 30
-32t + 30 = 0
32t = 30
t = 30/32 = 15/16

The ball is highest after 15/16 seconds

Answer 3

Take care to show negative sign when posting questions!

h(t) = - 16t² + 30t + 6

h ` (t) = - 32 t + 30 = 0 for turning point.

32t = 30

t = 30 / 32 = 15 / 16

h(15/16) = - 16 (15/16)² + 30 x 15/16 + 6

h(15/16) = 20 ft is maximum height.

Answer 4

i thinks this function is weird
with this function
there is not maximum height,there is only minimum height
and this minimum height is below the ground
you better check if you write the the function correctly