A girl drops a basketball off of a dam and it falls freely. Which of the following is true? The ball's kinetic energy increases by equal amounts in equal distances. The ball's kinetic energy increases by equal amounts in equal time intervals.
Question
A girl drops a basketball off of a dam and it falls freely. Which of the following is true? The ball's kinetic energy increases by equal amounts in equal distances. The ball's kinetic energy increases by equal amounts in equal time intervals.
Solution
The statement "The ball's kinetic energy increases by equal amounts in equal time intervals" is true.
Here's why:
When an object is in free fall, the only force acting upon it is gravity. This force causes the object to accelerate towards the earth at a constant rate, known as the acceleration due to gravity (approximately 9.8 m/s²).
Kinetic energy (KE) is given by the formula KE = 1/2 mv², where m is the mass of the object and v is its velocity. Since the velocity of the ball is increasing at a constant rate due to the constant acceleration, the increase in kinetic energy will be constant for each unit of time that passes.
On the other hand, the statement "The ball's kinetic energy increases by equal amounts in equal distances" is not necessarily true. This is because the rate of increase of the ball's kinetic energy is not constant with respect to distance. As the ball falls, it accelerates, so it gains kinetic energy more rapidly as it falls further. Therefore, the increase in kinetic energy is not the same for each unit of distance that the ball falls.
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