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Which table most likely relates the height, h(t), in meters, over time, t, in seconds, of a ball dropped from above ground level that hits the ground sometime between 4 and 6 seconds after it is dropped? A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 70, 50. 4, negative 8. 4, negative 106. 4. A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 100, 80. 4, 21. 6, negative 76. 4. A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries negative 150, negative 130. 4, negative 71. 6, 26. 4. A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 180, 160. 4, 101. 6, 3. 6.

Respuesta :

The table which most likely relates the height h(t), in meters, over time, t, in seconds  is: Option D:

  •        t (in seconds)            h(t) (in meters)
  •        0                                180
  •        2                                160.4
  •        4                                101.6
  •        6                                3.6

What are the values the height function can achieve if the object is always above the ground?

If the height function is function of time 't', and the object's height is measured from the ground level and object never goes inside ground, then that means height can never be negative. It will always assume non-negative values.

What are equations of motion?

There are three equations of motion that can be used when motion of the object is under constant acceleration and on a straight path.

They are listed below as:

[tex]v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as[/tex]

where the symbols have following meanings:

  • u = initial velocity of the considered object
  • v = final velocity of the object
  • a = acceleration of the object
  • s = distance traveled by the object in 't' time.

All the tables given except the last table have negative height values. That shows that if those negative valued tables are true, then the ball went inside ground.

Since no such event of ball going inside the ground is specified in the considered situation, thus, only the last table is valid here in terms of sign of height.

The last table is:

       t (in seconds)            h(t) (in meters)

       0                                180

       2                                160.4
       4                                101.6
       6                                3.6

Checking the truthfulness of the last table by using law of motion in straight path:

u = initial velocity of ball = 0

a = gravitational acceleration = -g ≈ -9.8 m/s sq.

Now, height of ball at time t = initial height of ball - distance it traveled from starting point in direction of reaching ground.

Thus, h(t) = 180 - |s| (assuming first value is true in the table)

where |s| = non-negative value of s

[tex]s= ut + (1/2)at^2\\s = 0t + (1/2)(-9.8)t^2\\\\|s| = 4.9t^2 \: \rm m/s^2[/tex]

Thus, h(t) = 180 - 5t² m/s sq.

[tex]h(2) = 180 - 4.9(2)^2 = 160.4\\h(4) = 180 - 4.9(4)^2 = 101.6\\h(6) = 180 - 4.9(6)^2 = 3.6\\[/tex]

Thus, the table which most likely relates the height h(t), in meters, over time, t, in seconds  is: Option D:

  •        t (in seconds)            h(t) (in meters)
  •        0                                180
  •        2                                160.4
  •        4                                101.6
  •        6                                3.6

Learn more about equations of motion here:
https://brainly.com/question/5955789

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