```Question 190845
Initial speed (velocity) of Vo will travel a distance of (s) meters,
where s=4.9t^2 + Vot and t is measured in seconds. Solve for t.
Use 4.9t^2 + Vot = s
:
4.9t^2 + Vot - s = 0
:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this equation: x = t ; a = 4.9, b = Vo, c = -s
:
{{{t = (-Vo +- sqrt(Vo^2 - 4 * 4.9 * (-s) ))/(2*4.9) }}}
:
{{{t = (-Vo +- sqrt(Vo^2 - (-19.6s) ))/(9.8) }}}
:
{{{t = (-Vo +- sqrt(Vo^2 + 19.6s ))/(9.8) }}}
:
;
Downward speed:
An object thrown downward from 200-m cliff travels 91.2m in 4 sec. What was the initial velocity of the object.
:
4.9t^2 + Vot = s
Substitute 4 for t and 91.2 for s
4.9(4^2) + 4Vo = 91.2
4.9(16) + 4Vo = 91.2
78.4 + 4Vo = 91.2
4Vo = 91.2 - 78.4
4Vo = 12.8
Vo = {{{12.8/4}}}
Vo = 3.2 m/sec
:
:
Check solution using Vo = 3.2 & s = 91.2 m
{{{t = (-Vo +- sqrt(Vo^2 + 19.6s ))/(9.8) }}}
;
{{{t = (-3.2 +- sqrt(3.2^2 + 19.6*91.2 ))/(9.8) }}}
:
{{{t = (-3.2 +- sqrt(10.24 + 1787.52 ))/(9.8) }}}
:
{{{t = (-3.2 +- sqrt(1797.76 ))/(9.8) }}}
:
Positive solution
{{{t = (-3.2 +42.4)/(9.8) }}}
t = {{{39.2/9.8}}}
t = 4 sec as given above
```