Question

Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. Assume the starting height of the ball is 0 feet. Approximately, how long does it take until the soccer ball hits the ground again?

1.3 secs

2.6 secs

16.0 secs

27.6 secs

Answer 1

what do we know that will helps us with this?

Answer 2

and is the initial velocity vertical? or angled?

Answer 3

vertical i tink

Answer 4

i think so too, its hard to come to a definitive result otherwise

Answer 5

this tends to be more of a physics question, seeing as how if it was mathical they provide more of a formula to solve

Answer 6

since our velocity is in feet; lets use gravity as -32 ft/sec/sec

Answer 7

this is a constant acceleration due to gravity on earth:

a(t) = -32

to get to velocity we need to "antiderive" or inegrate it up.

\[\int -32\ dt=-32t+C\]

Answer 8

that was odd ... computer went a little whacky

Answer 9

at time = 0; or t=0 we have a velocity of 42

v(0) = -32(0) + C = 42
C = 42

v(t) = -32t +42 .... so far so good

Answer 10

thank you

Answer 11

to get to position, or height, we need to up this one more time

Answer 12

\[\int -32t+42\ dt=-16t^2+42t+C\]

and since at t=0 we have a height of 0 ...

h(0) = -16(0)^2 +42(0) + C = 0
C = 0

h(t) = -16t^2 +42t

now we can solve for "t" that will give us a height of 0 ... you know, other than at t=0 :)

Answer 13

h(t) = -16t^2 +42t = 0
2t(-8t +21) = 0

t = 0 or t = 21/8, 2 5/8

Answer 14

id say 2.6 is a good bet

Answer 15

thank u very much

Answer 16

youre welcome :)