Find the vertical velocity of 48ft. per second from a height of 3ft. What is the maximum height? How many seconds does it take before it reaches its maximum height?

So, the formula for this is:

s(t) = -16t^2 + v_0t + s_0

where

s(t) = height at any given time t

v_0=initial velocity (v-naught)

s_0= Initial height (s-naught)

t = time in seconds

From this, we know initial height and initial velocity, so we plug those values in:

s(t) = -16t^2 + 48t + 3

So! From here, we know that the formula in question is a parabola, and we need the vertex. The vertex tells us the total time it took.

formula for vertex:

v = -b/2a = -48/(2*-16) = -48/-32 = 1.5s

1.5s to reach maximum height

Plug that into the formula:

s(t)=-16*(3)^2 + 48*3 + 3*3

s(t) = 144 + 144 + 9 = 297 ft

It will take 3 seconds to reach a maximum height of 297 ft :)

so is 1.5 or 3 seconds the time it takes before it reaches it maximum height?

Oh, it looks like I made a mistake! I am so sorry. It should be: 1.5 seconds to reach max height.

And max height is 39 ft, not 297. I doubled the value. You have my utmost apologies.

its alright everyone makes mistakes. you were still a big help! Thank you!

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