To determine whether the student's claim is correct, we need to understand how gravitational potential energy converts to kinetic energy as an object falls.
The kinetic energy (KE) of an object just before it hits the ground can be calculated using the formula:
\[ KE = mgh \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height from which the object is dropped.
From this formula, it's clear that the kinetic energy increases with height. Therefore, as the height from which the ball is dropped increases, its kinetic energy upon impact with the ground also increases.
Now, let's analyze the student's claim: she states that a ball dropped from 3.0 meters will have fewer than 96 joules of kinetic energy.
If we assume the mass of the ball is such that it would produce less than 96 joules at that height, we can analyze typical scenarios. For a standard mass, like 10 kg, KE would be calculated as follows:
\[ KE = 10 , \text{kg} \times 9.81 , \text{m/s}^2 \times 3.0 , \text{m} \] \[ KE = 10 \times 9.81 \times 3 \] \[ KE = 294.3 , \text{J} \]
This indicates that a ball of 10 kg dropped from 3.0 meters has 294.3 joules of kinetic energy, far exceeding 96 joules.
Thus, the correct answer is:
C She is wrong, the higher the drop, the more kinetic energy the ball will have upon hitting the ground.
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