SOLUTION: 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 Downward speed: An obje

Algebra ->  Radicals -> SOLUTION: 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 Downward speed: An obje      Log On


   



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
Downward speed:
An object thrown downward from 200-m cliff travels 91.2m in 4 sec. What was the initial velocity of the object.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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
:
Treat it as a quadratic equation, use the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation: x = t ; a = 4.9, b = Vo, c = -s
:
t+=+%28-Vo+%2B-+sqrt%28Vo%5E2+-+4+%2A+4.9+%2A+%28-s%29+%29%29%2F%282%2A4.9%29+
:
t+=+%28-Vo+%2B-+sqrt%28Vo%5E2+-+%28-19.6s%29+%29%29%2F%289.8%29+
:
t+=+%28-Vo+%2B-+sqrt%28Vo%5E2+%2B+19.6s+%29%29%2F%289.8%29+
:
;
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%2F4
Vo = 3.2 m/sec
:
:
Check solution using Vo = 3.2 & s = 91.2 m
t+=+%28-Vo+%2B-+sqrt%28Vo%5E2+%2B+19.6s+%29%29%2F%289.8%29+
;
t+=+%28-3.2+%2B-+sqrt%283.2%5E2+%2B+19.6%2A91.2+%29%29%2F%289.8%29+
:
t+=+%28-3.2+%2B-+sqrt%2810.24+%2B+1787.52+%29%29%2F%289.8%29+
:
t+=+%28-3.2+%2B-+sqrt%281797.76+%29%29%2F%289.8%29+
:
Positive solution
t+=+%28-3.2+%2B42.4%29%2F%289.8%29+
t = 39.2%2F9.8
t = 4 sec as given above