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# Consider the diagram below showing the trajectory of an object thrown from Point 0. Which of the following is true?

1. Potential energy is greatest at Point-2
2. Kinetic energy is least at Point-5
3. Kinetic energy is greatest at Point-0
4. Kinetic and Potential energies are the same at Points-0 and 4
5. At Point-1 Kinetic energy is decreasing and potential energy is increasing

Answer: Statements 1 and 5 are TRUE.
1. Potential energy greatest at Point-2 (TRUE). At the top of the trajectory, the object is at the greatest distance above the ground and hence has the greatest potential energy
2. Kinetic energy is least at Point-5 (FALSE). At the top of the trajectory, is the place with the least velocity, since the y-component of the velocity is zero, and hence the least kinetic energy.
3. Kinetic energy is greatest at Point-0 (FALSE). At the bottom of its trajectory, it has the greatest velocity and thus the greatest kinetic energy
4. Kinetic and Potential energies are the same at Points-0 and 4 (FALSE) From our study of kinematics, we know that the speed of a projectile is equal at the same height in the projectile’s ascent and descent. Therefore, the tomato has the same kinetic energy at points 1 and 3. Additionally, since the object has the same height at these points, its potential energy is the same at points 1 and 3.
5. At Point-1 Kinetic energy is decreasing and potential energy is increasing (TRUE). At this point, the velocity is decreasing in magnitude and the object is getting higher in the air. Thus, the kinetic energy is decreasing and the potential energy is increasing.

edited Aug 27, 2014