A skydiver jumps out of a plane and begins to accelerate. His speed increases to 20 m/s, then 30 m/s. His acceleration slows until he reaches a constant speed of 50 m/s. Which statement correctly describes his kinetic energy during this time?
1. His kinetic energy would remain the same for the whole fall as long as he lost no mass
2. His kinetic energy was positive at first, but it decreased to zero
3. His kinetic energy increased quickly at first, then it increased at a constant rate.
4. His kinetic energy increased while his speed increases, then it became constant
4. His kinetic energy increased while his speed increases, then it became constant.
The correct statement is:
4. His kinetic energy increased while his speed increases, then it became constant.
Explanation:
Kinetic energy is given by the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
In this scenario, the skydiver's speed increases from 0 m/s to 20 m/s, and then to 30 m/s. As the skydiver's speed increases, his kinetic energy also increases because the square of the velocity is directly proportional to the change in kinetic energy.
Once the skydiver reaches a constant speed of 50 m/s, his kinetic energy also becomes constant because his velocity (v) is no longer changing. Therefore, his kinetic energy remains constant at this point.
To answer this question, we need to understand the relationship between kinetic energy and speed.
Kinetic energy (KE) is given by the equation KE = (1/2) * mass * (speed)^2. It is directly proportional to the square of the speed of an object.
Let's analyze the given scenario:
1. Initially, the skydiver jumps out of the plane and starts to accelerate. As his speed increases from 0 to 20 m/s, his kinetic energy will increase because the speed is increasing. So, option 4 is correct in stating that his kinetic energy increased while his speed increased.
2. Then, the skydiver's speed increases further to 30 m/s. At this point, his kinetic energy continues to increase because the speed is still increasing. Therefore, option 4 is still the correct statement.
3. Finally, the skydiver's acceleration slows down, and he reaches a constant speed of 50 m/s. At this point, his kinetic energy will be at its maximum value and remain constant because the speed is no longer changing. Thus, option 4 is incorrect since the kinetic energy does not become constant; it remains constant after reaching its maximum value.
To summarize, option 4 is the correct statement. The skydiver's kinetic energy increased while his speed increased, and it remained constant once he reached a constant speed of 50 m/s.