### Throwing a Ball Up at the Edge of a Building

From the edge of a building, a ball is thrown upward with the vertical initial velocity of 19.6 m/s; when the ball returns to the lunching level (the roof of the building) it just miss the edge of the building and it continues falling down to the street level. Calculate the displacement and velocity of the ball 0s, 1s, 2s, 3s, 4s, and 5s after the ball is originally thrown.

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Solution:

In order to calculate the velocity of the ball, formula (F_F 3), , should be used; in this case, the initial velocity is . At the same time, the displacement of the ball can be calculated from formula (F_F 4), .

After substituting the initial conditions in the equations, the following formulas can be used for calculating the velocity and position at the different times,

 Velocity: Position:
 At time, t = 0, { The velocity and the displacement are the initial conditions for the motion. At time, t = 1, { Since the ball is moving upward and the acceleration of gravity is always downward, the ball is slowing down. Because the displacement of the ball is above the zero level, the displacement is positive. At time, t = 2, { At this time, the ball reaches what is called the maximum height. At this point in the motion the velocity of the ball is zero for an instant. At time, t = 3, { Now, the ball is falling down; thus, the velocity is negative. The magnitude of the velocity is increasing because both the velocity and acceleration of gravity are pointing in the same direction, down. At time, t = 4, { Here, the ball has returned to the launching point (displacement zero meter), the edge of the building, the velocity has the same magnitude as when launched. However, the sign is negative because the direction of the velocity downward, still the ball is speeding up because of the acceleration of gravity. In addition, at this point it can be seeing that the equation of motion represents the displacement not the distance traveled. In fact, at this point, the distance traveled is 39.2 m; where 19.6 m of that distance is coming from the motion up and 19.6 m coming from the motion down. At time, t = 5, { Finally, both, the velocity and the displacement are negative. The displacement is negative because the position of the ball is below the launching point. Notice that the ball is still speeding up due to the acceleration of gravity.

 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com