To determine how the kinetic energy of the bowling ball behaves as it is dropped from varying heights, we need to consider the relationship between gravitational potential energy and kinetic energy. When an object is dropped, its gravitational potential energy is converted into kinetic energy as it falls.
The gravitational potential energy (PE) at a given height \( h \) is given by the formula:
\[ PE = mgh \]
where:
- \( m \) is the mass (10 kg in this case),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height from which the object is dropped.
As the ball falls, this potential energy converts to kinetic energy (KE). When the ball reaches the ground, all the potential energy has been converted to kinetic energy, and it can be expressed as:
\[ KE = mgh \]
From this equation, we see that kinetic energy is directly proportional to height (\( h \)). Hence, as the height increases, the kinetic energy increases linearly.
Given this understanding, the correct representation of the ball's kinetic energy when dropped from 1 m, 2 m, and 3 m would be Option 1: A graph with kinetic energy increasing linearly with height.