A toy cannon tosses a rubber ball straight upward. A motion sensor measures the speed of the ball as it leaves the cannon. Using the conservation kinetic and gravitational potential energy, what can this information be used to calculate the mass

With this information is not possible to calculate the mass.

Explanation:

This is a characteristic problem of energy conservation, where kinetic energy becomes potential energy. For this particular problem, we have the initial speed as input data. The moment the ball comes out of the cannon we have the maximum kinetic energy, as the ball goes up the ball will gain more potential energy as the ball loses kinetic energy, until the moment the ball reaches the maximum height. At the maximum height point, the ball will have its maximum potential energy while its kinetic energy is zero. In other words, all the kinetic energy that was, in the beginning, was transformed into potential energy.

In the above equation the masses are canceled and we can determine the maximum height, by means of the initial speed.

But the mass cannot be determined, since it would be necessary to know the value of the energy, in order to determine the value of the mass.