To determine if the student's claim is correct, we need to understand how to calculate the kinetic energy (KE) of an object just before it hits the ground after being dropped from a height. The kinetic energy of an object is given by the formula:
\[ KE = mgh \]
where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the object (in kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) on the surface of the Earth),
- \( h \) is the height from which the object is dropped (in meters).
Assuming we know the mass of the ball, we can calculate the kinetic energy for a height of 3.0 meters.
- If we say the mass \( m \) of the ball is \( m \) kg, the kinetic energy at a height of 3.0 meters can be calculated as follows:
\[ KE = m \cdot g \cdot h = m \cdot 9.81 \cdot 3.0 \]
- Simplifying that gives:
\[ KE = 29.43m \]
- To determine if this value is less than 96 joules, we solve for \( m \):
\[ 29.43m < 96 \]
\[ m < \frac{96}{29.43} \approx 3.26 , \text{kg} \]
This means that if the mass of the ball is less than approximately 3.26 kg, then the kinetic energy of the ball when dropped from a height of 3.0 meters would indeed be less than 96 joules.
If the mass of the ball is greater than 3.26 kg, then the kinetic energy would be equal to or greater than 96 joules.
In conclusion, the student's claim can be correct or incorrect depending on the mass of the ball:
- If the ball's mass is less than 3.26 kg, her claim is correct (fewer than 96 joules).
- If the ball's mass is greater than 3.26 kg, her claim is incorrect (more than 96 joules).
Without additional information on the mass of the ball, we cannot definitively say whether her claim is right or wrong.
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