Question

A puppy was launched with upward velocity of 148ft/s the height of the puppy (h) in feet after (t) seconds is h=-16t^2+148t+30.
how do i get the maximum height?

Answer 1

Im not sure why there launching puppies...

Answer 2

Why would you need the maximum height?? CATCH THE PUPPY!!

Answer 3

I will! I need 2 know how high it can go for my evil math teacher though

Answer 4

2 ways to get the maximum height: the calculus way and the non-calculus way of simply getting the vertex form for the equation. Either method will work and the maximum height is achieved at

t = 4.625 seconds

So, just put that value of "t" into the equation and you will have your maximum height.

This works for objects other than puppies also!

Answer 5

Vertex method: Complete the square

y = -16(t^2 - 37t/4 - 15/8)

y = -16(t^2 - 37t/4 + [37/8]^2) + (16)(15)/(8) + (16)[37/8]^2

y = -16(t - 37/8)^2 + (16)(15)/(8) + (16)[37/8]^2

That first term, -16(t - 37/8)^2 is 0 at t = 37/8 = 4.625

So, the maximum is attained at that time since "0" is being subtracted from the rest of the right side, so your max height is:

(16)(15)/(8) + (16)[37/8]^2 = 372.25



Calculus method: (much easier)

Take the first derivative of the height equation:

h' = -32t + 148

set h' = 0 -> -32t + 148 = 0 -> t = 4.625

Put 4.625 into your original equation.

h = -16(4.625)^2 + 148(4.625) + 30

h = 372.25

Answer 6

If you haven't had calculus yet, then just go with the vertex (completing the square) method which uses only basic algebra. Either method gives the same answer.

Answer 7

Here's a nice graph where you can see that max:

Answer 8

All good now, @JaneDoe100 ?

Answer 9

O_O he's a wizard...

Answer 10

I'm no wizard! But I'm no puppy-launcher either!

Answer 11

Good luck to you in all of your studies and thx for the recognition! @JaneDoe100