Elaine shoots an arrow upward at a speed of 32 feet per second from a bridge that is 28 feet high. The height of the arrow is given by the function h(t) = -16t2+32t + 28, where t is the time in seconds.

Question

a. What is the maximum height that the arrow reaches?
b. How long does it take the arrow to reach its maximum height?
c. How long would it take before the arrow reached the ground? Round your answer to the hundredths place.

Answer 1

(b) as always, max height (the vertex) is at t = -b/2a = 1
(a) figure h(1)
(c) solve -16t^2+32t+28 = 0

Answer 2

step 1: this is a parabola, find the two zeroes.
0=-16t^2+32t+28
0=-(8t^2-16t-14)
=-(4t^2-8t-7)
going to the quadratic formula
t=(-b+-sqrt(b^2-4ac))/2a
a=4; b=-8, c=-7
t=(8+-sqrt(64+4*56)/8
t= 1+-16.1/8= 3 or t=-1

so where is the maximum height? Halfway between..t=(-1+3)/2 or at 1 second
max height=-16t2+32t + 28 at t=1 solve it
when will it hit the ground? t=3 as above