To determine if the student's claim is correct, we need to calculate the kinetic energy of the ball when it hits the ground after being dropped from a height of 3.0 meters. The kinetic energy (KE) of an object just before impact can be calculated using the formula derived from the principle of conservation of energy:
\[ KE = mgh \]
where:
- \( KE \) = kinetic energy (in joules)
- \( m \) = mass of the ball (in kilograms)
- \( g \) = acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \))
- \( h \) = height (in meters)
Assuming the mass of the ball is not provided, we can just express the kinetic energy dependent on the mass:
Plugging in the values:
\[ KE = mg(3.0 , \text{m}) = m \cdot 9.81 , \text{m/s}^2 \cdot 3.0 , \text{m} \] \[ KE = 29.43m , \text{joules} \]
To find out if the kinetic energy is less than 96 joules, we can set up the inequality:
\[ 29.43m < 96 \]
Now, solving for the mass \( m \):
\[ m < \frac{96}{29.43} \] \[ m < 3.26 , \text{kg} \]
This means that if the ball's mass is less than approximately 3.26 kg, then the kinetic energy at the moment of impact will be less than 96 joules.
If the ball has a mass greater than 3.26 kg, then it will have more than 96 joules of kinetic energy upon hitting the ground.
Thus, the student's statement that a ball dropped from a height of 3.0 meters would have less than 96 joules of kinetic energy when it hits the ground is only correct if the mass of the ball is less than 3.26 kg.
In conclusion, whether the student is correct depends on the mass of the ball. If the mass is known to be less than 3.26 kg, her claim is correct. If the mass is equal to or greater than 3.26 kg, then she is incorrect.
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