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Suppose a ball is thrown vertically upward (positive direction) from an initial height LaTeX: h_0 with initial velocity LaTeX: v_0. Find the position function LaTeX: s(t) of the ball after LaTeX: t seconds assuming the gravitational acceleration LaTeX: g is a positive constant pointing downward (negative direction).

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onyebuchinnaji

After time t, the position function of the ball is determined as [tex]y(t) = h_0\ +\ v_0t \ - \ \frac{1}{2} gt^2[/tex]

The given parameters;

  • initial velocity of the ball, = [tex]v_0[/tex]
  • initial position of the ball, = [tex]h_0[/tex]
  • acceleration due to gravity, = g

The position function of the ball after time t, is calculated as follows;

[tex]y(t) = h_0\ +\ v_0t \ - \ \frac{1}{2} gt^2[/tex]

The negative sign of acceleration of due to gravity is because the ball is moving upward against gravity.

Thus, after time t, the position function of the ball is determined as [tex]y(t) = h_0\ +\ v_0t \ - \ \frac{1}{2} gt^2[/tex]

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