posted by Selena on .
A ball is thrown into the air. The height in feet of the ball can be modeled by the equation h = -16t2 + 20t + 6 where t is the time in seconds, the ball is in the air. When will the ball hit the ground? How high will the ball go?
16 t^2 -20 t - 6 = - h in obsolete English units
when does h = 0?
t = [ 20 +/- sqrt (400 + 384) ] /32
t = [ 20 +/- 28 ] /32
t = 48/32 = 1.5 seconds (ignore the negative t)
for vertex complete the square assuming no calculus may be used
16 t^2 -20 t = - h + 6
t^2 - (5/4) t = -h/16 + 3/16
t^2 - (5/4)t + 25/64 = -4h/64 + 37/64
(t-5/8)^2 = -(4/64) (h - 148 )
max height = 148 at t = 5/8 sec
Find the vertex of the parabola by completing the square:
which means that the vertex is at
and it will hit the ground at h(t)=0, or
t=3/2 s (rejecting negative root).
Maximum is at the vertex, or
thanx both of yall XD