Height of a thrown (or launched) body at time \(t\). The height is the vertical distance to the ground.

Initial height

$$ y_0 $$ Unit $$ \mathrm{m} $$

Initial height from which a body is thrown.

Initial vertical velocity

$$ v_{\text y0} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$

Initial velocity in vertical direction. For example, the body could have been thrown at an angle, which is why it has a velocity \(v_{\text y0}\). The total velocity of the body is \( v_0 = \sqrt{ v_{\text y0}^2 ~+~ v_{\text x0}^2 } \) with \(v_{\text x0}\) as initial velocity in the horizontal direction.

Time

$$ t $$ Unit $$ \mathrm{s} $$

If you insert a time \(t\) into the formula, you get the current height position \(y(t)\) of the body.

Gravitational acceleration

$$ g $$ Unit $$ \frac{\mathrm{m}}{\mathrm{s}^2} $$

Gravitational acceleration is an acceleration of the body due to gravity. On earth it has the value \( g = 9.8 \, \frac{\mathrm m}{\mathrm s^2} \). The minus sign in the formula says that the gravitational acceleration is directed against the \(y\)-axis ("upwards"), which here points against the falling motion.

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