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To find time "t", you need solve this quadratic equation
-4.9t^2 + 19.6t = 14.7 meters.
Simplify it step by step
-4.9t^2 + 19.6t - 14.7 = 0
Divide by (-4.9) both sides
t^2 - 4t + 3 = 0
Factor left side
(t-3)*(t-1) = 0.
There are two positive roots t= 1 second and t= 3 seconds.
First root is for the ball moving vertically up; the second root is for the ball falling down.
Solved, with complete explanations.
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To see many other similar solved problems, look into the lessons
- Problem on a projectile moving vertically up and down
- Problem on an arrow shot vertically upward
- Problem on a ball thrown vertically up from the top of a tower
- Problem on a toy rocket launched vertically up from a tall platform
in this site.