Why Is the Initial Speed of a Ball Thrown Vertically 19 m/s?

AI Thread Summary
To determine the initial speed of a ball thrown vertically that is caught 3.0 seconds later at a height of 14 meters, it is essential to use the correct kinematic equations. The average velocity calculated (4.7 m/s) does not represent the initial velocity, as it only gives the average over the entire motion. The initial speed must account for the ball's acceleration due to gravity, which affects its speed after being thrown. The correct approach involves using the kinematic equation that incorporates initial velocity, acceleration, and displacement. The study guide's answer of 19 m/s reflects the necessary calculations for vertical motion under gravity.
athena04
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A ball thrown vertically from ground level is caught 3.0 s later by a person on a balcony who is 14 m above the ground, determine the initial speed of the ball.

When I first tried doing this problem, I tried using the speed equation of distance/change in time, so I divided 14 by 3 which gave me 4.7 m/s, but according to my study guide the answer is 19 m/s and I'm having a hard time understanding why that's the answer and what equation I would use to solve it. Any help is appreciated, thanks!
 
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Hi athena, welcome to PF!

If you are using displacement = average velocity * time, your result is the average velocity, not the initial velocity. Can you find another equation to use from the list of the kinematic motion equations?
 
What happens to the speed of the ball after it leaves the thrower's hand?
 
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