Dona rolls a marble with a speed of 5.0/m/s across a level table that is 1.6m above the floor. upon reaching the edge of the table it follows a parabolic path to the floor . how far does the marble travel in the x direction

We have that for the Question "Dona rolls a marble with a speed of 5.0/m/s across a level table that is 1.6m above the floor" it can be said that the travel in the x direction is

x'=2.85m

From the question we are told

Dona rolls a marble with a speed of 5.0/m/s across a level table that is 1.6m above the floor. Upon reaching the edge of the table it follows a parabolic path to the floor . How far does the marble travel in the x direction

Generally the equation for the kinematic equation  is mathematically given as

t=0.57s

Therefore

The Horizontal distance

x'=2.85m

For the QUestion"How far does the marble travel in the x direction"

x'=2.85m

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2.9 m

Explanation:

First find the time it takes to reach the floor.

y = y₀ + v₀ t + ½ at²

(0 m) = (1.6 m) + (0 m/s) t + ½ (-9.8 m/s²) t²

t = 0.571 s

Next, find the distance it travels in that time.

x = x₀ + v₀ t + ½ at²

x = (0 m) + (5.0 m/s) (0.571 s) + ½ (0 m/s²) (0.571 s)²

x = 2.86 m

Rounded to two significant figures, the marble travels 2.9 meters in the x direction.

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0.19 m/s and 0.45 m/s