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Vertical motion

Graphical representation of our solution

Height y(t) of the solid metal ball as a function of the time t at intervals of 0.1 seconds.		Velocity v(t) of the solid metal ball as a function of the time t at intervals of 0.1 seconds.

In the above figures we represent graphically the motion of the solid metal ball as it is given by our solution for the dynamical equation of objects moving freely and vertically in vacuum under the influence of the gravitational attraction near the surface of the Earth.

In the lefthand-side figure we show how the height varies with time. The figure sets out at t=0 seconds where the height of the ball equals y₀=0 metres and where its initial upward speed is measured to be given by v₀=20 m/s. At first the solid metal ball rises fast in time, but then it slows down untill it reaches its maximum position at about 20 metres height. From thereon the solid metal ball starts falling towards the Earth with increasing velocity, thereby reducing its height. The quadratic time dependence of y results in a parabolic curve in the t-y graph for the motion of solid metal ball.

In the righthand-side figure we show how the velocity varies with time. The linear time dependence of v results in a straight-line curve in the t-v graph for the motion of solid metal ball. Somewhere near t=2 seconds, where the solid metal ball reaches its maximum height, its velocity vanishes. Before reaching its maximum height the velocity of the solid metal ball is upward, hence positive, whereas, after reaching its maximum height the velocity of the solid metal ball is downward, hence negative.

B=0