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A baseball is thrown up in the air. The table shows the heights y (in feet) of the baseball after x seconds. Write an equation for the path of the baseball. Find the height of the baseball after 1.7 seconds. ​

Ill mark branliest also I need work shown pleaseA baseball is thrown up in the air The table shows the heights y in feet of the baseball after x seconds Write class=

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Y=1/2x+18 GIVE ME BRAINSLIST NOW

The equation of an object in free fall is the equation of a parabola

  • The equation for the path of the ball is y = -16·x² + 36·x + 4
  • The baseball height, after 1.7 seconds is 18.89 feet.

The reason the above values are correct are as follows:

The known parameters are;

The direction of the baseball is up in the air

The values of the height of the baseball after x seconds is given as follows;

[tex]\begin{array}{ccc}\mathbf{Time, \ x}&&\mathbf{Baseball \ height, \ y}\\0.5&&18\\1&&24\\1.5&&22\\2&&12\end{array}\right][/tex]

  • Required;

To write the equation for the path of the baseball

Solution:

The general equation of the motion of free fall is the equation of a parabola, which can be written as follows;

y = a·x² + b·x + c

From the given table, we have;

18 = a·0.5² + b·0.5 + c = 0.25·a + 0.5·b + c

18 =  0.25·a + 0.5·b + c...(1)

24 = a + b + c...(2)

22 = 2.25·a + 1.5·b + c...(3)

12 = 4·a + 2·b + c...(4)

Subtracting equation (1), from (2), to get equation (5) and subtracting equation (3) from (4) to get equation (6) gives;

6 = 0.75·a + 0.5·b...(5)

-10 = 1.75·a + 0.5·b...(6)

Subtracting equation (5) from equation (6) gives;

-10 - 6 = 1.75·a - 0.75·a = a

a = -16

From equation (5), we get;

6 = 0.75 × (-16) + 0.5·b

b = (6 - 0.75 ×  (-16))/0.5 = 36

b = 36

From equation (2), we get;

24 = (-16) + 36 + c

c = 24 - ((-16) + 36) = 4

The equation for the path of the ball is y = -16·x² + 36·x + 4

  • Required;

The height of the baseball after 1.7 seconds

Solution:

The height, y, of baseball after 1.7 seconds is given by substituting for the time x = 1.7 in the equation of the baseball as follows;

After 1.7 seconds, y = -16 × 1.7² + 36 × 1.7 + 4 = 18.89

The height of the baseball y, after 1.7 seconds is 18.89 feet.

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