If h(t) represents the height, in feet, of a ball and t represents time in seconds ,what is the interpretation of h(6) = 42?

Answer 1

h = height in feet

t = time in seconds

h(6 seconds) = 42

(6)           (6)

h = 7 feet

Answer 2

after 6 seconds the ball is 42 feet high

if the ball was thrown upwards at velocity = vo from ground level

then the formula is

h(t) =(a/2)t^2 + vot +ho, ho=0, for a typical function that reflects the force of gravity with a=-32 ft/sec/sec

h(6) = 42 = -16(6^2) + vo(6)

6vo = 42 + 16(36) = 42+576 = 618

vo = 618/6 = 103 ft per second = initial vertical velocity

formula for height is then

h(t) =-16t^2 +103t

h(6) =-16(6^2) +103(6)

= -16(36)+618

=618-576

= 42 feet high at 6 seconds

also h

=42 feet high in a fraction of a second, as it initially goes up

max height is when t=103/32 = 3 7/32 seconds

it hits the ground in exactly twice that time = 6 7/16 seconds

at 6 seconds it's coming down to 42 feet and just about half a second away from ground zero

-16t^2 +103t

complete the square

-16(t2- 103t/16 + (103/32)^2) + 16(103/32)^2

= -16(t-103/32)^2 +103^2/64

= -16(t- 3 7/32)^2 + 10609/64

vertex =about (3.22, 165.8)

max height = about 165.8 feet in 3.22 seconds

h= -16(103/32)^2 +103(103/32)

=103^2/64

=10609/64

=about 165.8 feet max height