An object was shot up into the air at an initial vertical speed of 384 feet per second. Its height as time passes can be modeled by the quadratic function f, where f(t)=−16t2+384t.

Question

An object was shot up into the air at an initial vertical speed of 384 feet per second. Its height as time passes can be modeled by the quadratic function f, where f(t)=−16t^2+384t. Here t represents the number of seconds since the object’s release, and f(t) represents the object’s height in feet.

After ______ seconds, this object reached its maximun height of ____ feet.

Answer 1

h(t)=-16t^2+384t

h'(t)=-32+384=0

t=384/32= 12 seconds

h(12)=-16(12)^2+384(12)

=16(144)

=2304 feet = max height