If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 80ft/s, its height h after t s is given by . How long does it take the ball to return to the ground?
2007-10-29 15:03:39 · 12 answers · asked by Amanda K 1 in Science & Mathematics ➔ Mathematics
First things first - calculate the time it would take for the velocity to reach zero.
Using that time, calculate distance travelled.
Add five feet (initial height). That will give you final height.
So now you have h - the height it was at when it stopped moving upward and began its trip downward.
Calculate the time it takes to fall that far.
Add that time to the first time you calculated.
Ta-da.
2007-10-29 15:08:13 · answer #1 · answered by Brian L 7 · 1⤊ 1⤋
First consider air resistance to be neglected.
The time of flight in moving up covering the same distance is the same as the time in moving down.
g = (final V – initial V)/ t
-32 = (0 –80) / t
t = 2.5 s
The time it takes for its course up and down back to its initial height is:
t= 2.5 x 2 = 5.0 seconds
TAKE NOTE, it started with an initial height of 15 ft, so the ball takes extra more time downward in covering the 15 ft distance with initial velocity of 80 ft/sec.
h =(Vi) (t) + (1/2)g (t^2) where: g=-32 ft/s/s Note: Use (-h) and (-V) for downward directions
-15 = -80t + (1/2)(-32) t^2 expressing it positively:
15 = 80t - (1/2)(-32) t^2 or expressing it in quadratic form
0 = 16 t^2 + 80 t -15
t = {-(80) +/- sqrt [80^2 - 4(16)(-15) ] } / { 2 (-16)}
t = {-80 +/- 73.76 } / { 2 (-16)} choosing the positive root
t = {-80 + 73.76 } / { 2 (-16)}
t = {-6.24}/{ 2 (-16)}
t = 0.195 seconds
Thus the total time is
T = 5.0 s + 0.195 s = 5.2 s
Please verify with your calculator.
2007-10-29 16:25:48 · answer #2 · answered by rene c 4 · 0⤊ 0⤋
Sounds like Physics. I think there's a formula to find out the time it hits the ball....look thru ur notes,and the book...chances are, your teacher may have gone over the problems but with different numbers. GOOD LUCK!
2007-10-29 15:07:30 · answer #3 · answered by <3 5 · 0⤊ 1⤋
because this is a ffree fall...the formula is
s=(u) (t)+1/2 (a) (t)^square
s=5 ft
u=80
a= earth gravity .. 9.8m/s^-2
t= time
5=80t + 1/2 (9.8) t^square
juz find the t = time..
2007-10-29 15:17:45 · answer #4 · answered by Anonymous · 0⤊ 1⤋
5 minutes.
2007-10-29 15:06:42 · answer #5 · answered by jessica.lanelle 4 · 0⤊ 2⤋
I did this last year. But I don't know what it is. I think it's something with exponents.
My name is Amanda K. too. Weird.
2007-10-29 15:07:53 · answer #6 · answered by User 3 · 0⤊ 1⤋
it would hit the ground at the rate of seven bleeting cats
2007-10-29 15:07:59 · answer #7 · answered by Anonymous · 1⤊ 1⤋
it depends what planet your on. if its on an asteroid it would fly off into space.
2007-10-29 15:15:06 · answer #8 · answered by The dude 3 · 0⤊ 1⤋
oh god. i wouldn' t know. i'm only in geometry. hell i have trouble with proofs. sorry.
2007-10-29 15:06:43 · answer #9 · answered by somexmusician 2 · 0⤊ 1⤋
it doesnt, the space mexicanas stole it
2007-10-29 15:06:37 · answer #10 · answered by Anonymous · 1⤊ 2⤋