The student says 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 she correct and why?
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No, the student is not correct. The kinetic energy of an object can be determined using the equation KE = 1/2mv^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object. The height from which the ball is dropped does not directly determine its kinetic energy. However, it can indirectly affect the kinetic energy if it affects the velocity of the ball. In this case, assuming no air resistance, the velocity of the ball when it hits the ground can be determined using the equation v = sqrt(2gh), where g is the acceleration due to gravity and h is the initial height. Substituting the given values, v = sqrt(2*9.8*3) = 7.67 m/s. Assuming the mass of the ball to be 1 kg, the kinetic energy can be calculated as KE = 1/2 * 1 * (7.67)^2 = 29.4 J. Therefore, the ball would have less than 96 joules of kinetic energy when it hits the ground.