To determine if the student's claim is correct, we need to analyze the kinetic energy of the ball as it falls. When an object is dropped from a height, its potential energy (PE) at that height is converted to kinetic energy (KE) as it falls, assuming air resistance is negligible.
The potential energy at a height \( h \) is given by the formula:
\[ PE = mgh \]
where:
- \( m \) is the mass of the ball,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height in meters.
Upon hitting the ground, this potential energy becomes kinetic energy. Therefore, the kinetic energy can be calculated as follows:
\[ KE = PE = mgh \]
Now, let's evaluate the student's claim:
- She claims that a ball dropped 3.0 meters would have fewer than 96 joules of kinetic energy.
Assuming the mass of the ball is necessary to check the student's claim, let's calculate the kinetic energy when the ball is dropped from a height of 3.0 meters.
To find the mass required for the kinetic energy to be 96 joules, we set up the equation:
\[ mgh = 96 \]
Substituting the values:
\[ mg(3.0) = 96 \] \[ m \times 9.81 \times 3.0 = 96 \] \[ m \times 29.43 = 96 \] \[ m = \frac{96}{29.43} \approx 3.26 , \text{kg} \]
This means that if the ball's mass is around \( 3.26 , \text{kg} \) or more, the kinetic energy upon hitting the ground would be equal to or greater than 96 joules. If the ball's mass is less than \( 3.26 , \text{kg} \), the kinetic energy will be less than 96 joules.
Ultimately, the student's claim depends on the mass of the ball. However, given any standard mass for a ball, it's quite likely that a typical ball (for instance, a baseball weighing about 0.145 kg) will have more than 96 joules of kinetic energy when dropped from 3.0 meters.
So, the correct response is:
She is wrong. The higher the drop, the more kinetic energy the ball will have upon hitting the ground.