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**1. Problem Statement**

A 2 kilogram block rests at the edge of a platform that is 10 meters above level ground.

The block is launched horizontally from the edge of the platform with an initial speed of

3 meters per second. Air resistance is negligible. The time it will take for the block to

reach the ground is most nearly

## Homework Equations

The kinematic equations, specifically to find the final velocity

V

_{f}

^{2}= V

_{i}

^{2}+2aΔX (to find the final velocity)

t=(V

_{f}-V

_{i})/2

## The Attempt at a Solution

I believe that the motion in the x direction is irrelevant. I also know that the acceleration is roughly 9.8 (m/s)/s in the direction toward the ground. So I know that the time it should take to go 10 meters is 1 second. However my calculations produce a final velocity of 14 m/s. Thus the time it takes is 1.4 seconds as the final and initial velocities summed is 14 m/s and that divided by 9.8 (m/s)/s is 1.42 seconds. I was able to produce this result knowing that the initial velocity in the Y direction is 0 m/s and that the acceleration and distance are 9.8 (m/s)/s and 10 m respectively. This calculation provides a result of 14 m/s as the final velocity and the time as 1.42 seconds.

This means that the velocity of the object increased by 4.2 m/s over .2 m. I made this conclusion based on the fact that in 1 second the object will have a velocity of 9.8 m/s. So it seems unrealistic that the object that took 1 second and 9.8 meters to accelerate to 9.8 m/s would suddenly accelerate to a velocity of 14 m/s over the course of .2 meters.

I am not sure what I am doing wrong, I believe I may be incorrectly applying the kinematic equations. I know the kinematic equations can be used when the velocity or acceleration is constant which it is here in the y component. I know this because the force of gravity is the only force acting on the object as it's in free-fall. The only error that I can see myself having is from the square root of the 2aΔX (because the acceleration value is negative thus providing a non-real answer). But I believe I could report the acceleration as a scalar descriptive quantity here. That being said I could very well be wrong.

I would appreciate some help. Thank you all very much. Also I apologize if there are any glaring errors or grammatical errors.

-John

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