Physics

Problem

At a certain instant a

1.5\,\text{kg}

ball moving vertically upward has a speed of

4\,\text{m/s}

. Its total mechanical energy with respect to the ground at that instant is

100\,\text{J}

. Take

g = 9.8\,\text{m/s}^2

. a. (a) Calculate the kinetic energy of the ball at that instant. b. (b) Hence find its gravitational potential energy with respect to the ground. c. (c) Determine the height of the ball above the ground at that instant.

Intuitive explanation

The key here is understanding that total mechanical energy is the sum of kinetic and potential energy, and it stays constant (assuming no air resistance). You know the ball's kinetic energy right now from its speed, so you can find its height by using $E_{\text{total}} = KE + PE$ and solving for the gravitational potential energy term $mgh$ . This height tells you where the ball is at this instant.

Intuitive explanation

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