To determine whether the student's claim is correct, we need to analyze the kinetic energy of the ball when dropped from a height of 3.0 meters. The kinetic energy (KE) of an object just before it hits the ground can be calculated using the formula:
\[ KE = mgh \]
where:
- \( KE \) is the kinetic energy in joules,
- \( m \) is the mass of the ball in kilograms,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height from which the ball is dropped in meters.
Given this formula, we notice that the kinetic energy depends on both the height from which the ball is dropped and the mass of the ball. Without knowing the mass of the ball, we cannot definitively calculate the kinetic energy.
To investigate her claim, let's assume the mass of the ball varies but we need to find a condition where the total kinetic energy is less than 96 joules. Rearranging our formula gives us:
\[ m < \frac{KE}{gh} \]
Substituting the values:
\[ m < \frac{96, \text{joules}}{9.81, \text{m/s}^2 \times 3.0, \text{m}} \] \[ m < \frac{96}{29.43} \] \[ m < 3.26 , \text{kg} \]
This means that if the mass of the ball is less than about 3.26 kg, then the kinetic energy upon hitting the ground when dropped from 3.0 meters would indeed be less than 96 joules.
In conclusion, the student's claim could be correct depending on the mass of the ball. If the ball's mass is less than approximately 3.26 kg, then it will have fewer than 96 joules of kinetic energy upon hitting the ground. If it's 3.26 kg or more, it will not. Therefore, without additional context on the ball's mass, we cannot definitively say whether the student's claim is correct; it is conditionally true.
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