Question

A group of engineering students construct a potato cannon. The height, h metres, of a potato t seconds after it is shot from the cannon that is on the roof of a building is modeled by the equation. h= -5(t-2)^2 + 45 a) how high is the potato after 1 s? b)when does the potato reach its maximum height? what is the height ? c) How long is the potato in the air?

Answer 1

a) is the simplest, since it's asking for h at t = 1 second, you can plug in t = 1 into the equation and evaluate h

b) you'll need to find the vertex of the parabola.

for vertex form equations y = (x-h)^2 + k, the vertex is (h,k) (note: don't confuse this h with height)

compare this to your equation

h= -5(t-2)^2 + 45 to determine your h and k values. h is the time it takes to reach the max height, and k is the max height

c) if you think about the trajectory of the potato, it starts at t = 0 and reaches height = 0 at some positive t-value. to find that t-value, simply take the equation h= -5(t-2)^2 + 45, set h = 0 and solve for t

I know this is a lot, but please let me know if you're having trouble with any of these individual steps or simply want to check your solution