Understanding Kinematic Equations in Physics

Two students are on a balcony a distance h above the street. One student throws a ball vertically downward at a speed vi; at the same time, the other student throws a ball vertically upward at the same speed.

Answer the following symbolically in terms of vi, g, h, and t. Write the kinematic equation for the y-coordinate of each ball. Final answer: Physics dictates that the y-coordinate for the ball thrown upwards is calculated by the equation y = h + vit - 0.5gt^2. For the ball thrown downwards, the y-coordinate is calculated as y = h - vit - 0.5gt^2. These calculations consider time, height above street, gravitational acceleration, and initial velocity. Explanation: The scenario describes two motions: upward motion and downward motion. The kinematic equations will be based on the equations of motion. The convention taken here is upward is positive.
  1. For the ball thrown upwards: y = h + vit - 0.5gt^2

    2. This equation considers initial velocity (vi), gravitational acceleration (g), height above the street (h), and time (t).

  2. For the ball thrown downwards: y = h - vit - 0.5gt^2

    3. This is because the initial velocity (vi) is in the negative direction i.e., downward.

Note that 'y' gives the y-coordinate of each ball at a given time. The directions in both equations are taken with respect to the ground.

Question: What is the kinematic equation for the y-coordinate of a ball thrown upwards and downwards in physics? Answer: The kinematic equation for the y-coordinate of a ball thrown upwards is y = h + vit - 0.5gt^2, while for a ball thrown downwards, it is y = h - vit - 0.5gt^2.
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