You can
put this solution on YOUR website! A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20 m/s.
When will the ball reach a height of 80m?
I would appreciate help with this one. Thank you!
The formula for the height h is
h = h0 + v0t - 4.9t²
h = the final height = 80 m
where h0 = the initial height = 100 m
v0 = the initial velocity = 20 m/s
t = the time to reach height h, so t is unknown.
h = h0 + v0t - 4.9t²
80 = 100 + 20t - 4.9t²
4.9t² - 20t - 20 = 0
Solve by the quadratic formula:
Use the quadratic formula:
______
-b ± Öb²-4ac
t = —————————————
2a
where a = 4.9; b = -20; c = -20
___________________
-(-20) ± Ö(-20)²-4(4.9)(-20)
t = ———————————————————————————————
2(4.9)
_______
20 ± Ö400+392
t = ———————————————
9.8
___
20 ± Ö792
t = ————————————
9.8
_____
20 ± Ö36·22
t = —————————————
9.8
__
20 ± 6Ö22
t = ———————————
9.8
Using the +,
__
20 + 6Ö22
t = ———————————
9.8
t = 4.912499445 seconds
Using the -,
__
20 - 6Ö22
x = ———————————
9.8
x = -.8308667917 seconds
We discard that negative answer, so the final answer is:
4.912499445 seconds
or you would probably want to round that to 4.9 seconds.
Edwin
