The height in feet of a golf ball hit into the air is given by #h= -16t^2 + 64t#, where t is the number of seconds elapsed since the ball was hit. What is the maximum height of the ball?

2 Answers
salamat
Mar 20, 2017

#64# feet

Explanation:

#h = -16 t^2 + 64 t#

maximum or minimum height when #h' =0#

#h' = -32 t + 64#

when #h' =0, -32 t + 64 =0#

#32 t = 64#, #t = 64/32 = 2#

#h'' = -32#, and since #h''# has a -ve value, therefore #h# is maximum when #t = 2#

when t =2,
#h = -16 (2)^2 + 64 (2)#
#h = -16 (2)^2 + 64 (2)#
#h = -16 (4) + 64 (2) = -64 + 128 = 64#

Jim G.
Mar 20, 2017

#64" feet"#

Explanation:

Find the roots of the parabola by setting h = 0

#rArr-16t^2+64t=0#

Factorising gives.

#-16t(t-4)=0#

#rArrt=0" or " t=4#

Since the parabola is symmetrical the axis of symmetry will pass through the maximum. The axis of symmetry is positioned at the mid- point of the roots.

#rArrcolor(red)(t=2)#

#rArr"max. height "=-16color(red)((2))^2+64(color(red)(2))#

#color(white)(xxxxxxxxxxxx)=(-16xx4)+(64xx2)#

#color(white)(xxxxxxxxxxxx)=-64+128#

#color(white)(xxxxxxxxxxxx)=64#

#rArr"maximum height of ball " =64" feet"#

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