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

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SUMMARY

The initial speed of a ball thrown vertically to reach a height of 14 meters in 3.0 seconds is 19 m/s. This conclusion is derived from the kinematic equations of motion, specifically using the equation for displacement, which incorporates initial velocity, acceleration due to gravity, and time. The average velocity calculated by dividing the height by time (4.7 m/s) does not represent the initial velocity, as it does not account for the effects of gravity on the ball's motion.

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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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