## six baseball throws are shown below. in each case the baseball is thrown at the same initial speed and from the same height h above the ground. assume that the effects of air resistance are negligible. rank these throws according to the speed of the baseball the instant before it hits the ground.

# six baseball throws are shown below. in each case the baseball is thrown at the same initial speed and from the same height h above the ground. assume that the effects of air resistance is negligible. rank these throws according to the speed of the baseball the instant before it hits the ground.

# They are all equilvalent

This answer is best understood in terms of conservation of energy. The initial energy of the ball is independent of the direction in which it is thrown.

The initial and final potential energies of the ball are the same regardless of the trajectory. Therefore, the final kinetic energy, and therefore the final speed, of the ball must be the same no matter in what direction it is thrown.

Hint A.1 How to approach the problem Although this situation can be investigated using the concepts of projectile motion, the conservation of mechanical energy is a better approach. Consider the initial total energy (kinetic plus gravitational potential).

By conservation of energy, the final total energy must be equal to the initial total energy. You can use the final energy to determine the final speed when it reaches the ground. Note that the launch angle does not affect the initial kinetic or initial gravitational potential energy of the ball.