word problem help

Question

the question i need help with is

"The distance d in meters traveled by a skateboard on a ramp is related to the time traveled in t in seconds. This is modeled by the function d(t)= 4.9t² - 2.3t + 5. what is the maximum distance the skateboard can travel and at what time would it achieve the distance?"
 If you could please explain this to me as best as you can that would be great. thank you.

Answer 1

-4.9t^2 +2.3t +5 (you have to switch the signs of t^2 and t for the problem to make sense, it would be even easier if the t coefficient were 3.2 ot -2.3)

-4.9t^2 +3.2t +5

take the derivative and set = 0

-9.8t +3.2 = 0

t = 3.2/9.8 = 1/3 seconds to reach max height

max height = -4.9(1/3)^2 + 3.2(1/3) + 5 = 5 +1.5/9 = 5.1666... meters high on the ramp. It goes up slightly then goes back down the ramp.

-9.8 meters per second per second is the effect of gravity.

3.2 meters per second is the initial velocity up the ramp

5 meters = the initial height

BUT if you want to keep the problem the way it's written

d(t) = 4.9t^2 + 2.3t + 5, the max distance traveled down the ramp is the length of the ramp

which is unknown as d could be infinity