find all values of t for which h = 5 feet?

Question

When a ball is thrown, its height in feet h after t seconds is given by the equation
h = vt – 16t^2 ,
where v is the initial upwards velocity in feet per second. If v = 19 feet per second, find all values of t for which h = 5 feet. Do not round any intermediate steps. Round your answer to decimal places.
(If there is more than one answer, enter additional answers with the "or" icon.)

Answer 1

h = vt – 16t^2

v = 19, h = 5

Hence, 5 = 19t – 16t^2 or 16t^2 - 19t + 5 =0

Using quadratic formula to solve this

t = [19 +/- sqrt(19^2 - 4*16*5)]/(2*16)

Therefore either t = 0.794 sec or t = 0.394 sec.

Answer 2

h=5 and v=19
so the equation will be
5 = 19t - 16t^2
16t^2 - 19t + 5 =0
divide both sides by 16
t^2 - 19/16 t + 5/16 = 0
completing the square
t^2 - 19/16 t + (19/32)^2 - (19/32)^2 + 5/16 = 0
(t - 19/32)^2 - (361/1024 - 320/1024) = 0
(t - 19/32)^2 - 41/1024 = 0
(t - 19/32 - srt41/32)(t - 19/32 + sqrt41/32) = 0
t = sqrt41/32 + 19/32 = 0.79 sec
t = 19/32 - sqrt41/32 = 0.39 sec

Answer 3

equation h = vt - 16t^2
where h = 5 and v = 19

substituting,
5 = 19t - 16t^2

16t^2 - 19t + 5 = 0

since it cant be resolved as such we use the formula

[-b +/- sqrt(b^2 - 4ac)]/2a
here

a=16 ; b= -19 ; c= 5

substituting i n the formula

[19 +/- sqrt{(-19)^2 - 4x16x5}]/2x16

[19+/- sqrt(361 - 320)]/32

[19 +/- 6.4031]/32

[19 + 6.4031]/32 or [19-6.4031]/32

0.793846875 or 0.393653125

The possible values of t are 0.393653125 or 0.793846875

Answer 4

.79feet/sec
or
.3936feet/sec