Question

A ball is thrown vertically upward with an initial velocity of 48 feet per second. The distance s​ (in feet) of the ball from the ground after t seconds is s = 48 t -16 t ^2. ​(a) At what time t will the ball strike the​ ground? ​(b) For what time t is the ball more than 32 feet above the​ ground?

Answer 1

Hello,

s=48t-16t²

a)
s=0==>16t(3-t)=0==>t=0 or t=3

b)
s>32==>48t-16t²>32===>16(t²-3t+2)<0
Δ=9-8=1
==>16(t-1)(t-2)<0

==>1<t<2 (negative between the roots)