A baseball is thrown straight up with initial speed

[bugbug]

A baseball is thrown straight up with initial speed v(o). If air resistance cannot be ignored, when the ball returns to its initial height its speed is less than v(o). Explain why, using energy concepts.
I am very confused as to why this is.

A projectile has the same initial kinetic energy no matter what the angle of projection. Why doesn't it rise to the same maximum height in each case?

Is it because the velocity in the x-direction is different?

 

[f95toli]

If air resistance cannot be ignored,

What happens when the ball travels through the air?¨
Also, if the ball is thrown straight up the x-coordidate will not change.

 

[m2003]

I can explain the phenomenon you described using energy concepts. When a baseball is thrown straight up with an initial speed v(o), it has both kinetic energy and potential energy. As it rises, the kinetic energy is converted into potential energy due to the force of gravity acting on it. However, when air resistance is present, it acts as a dissipative force and reduces the kinetic energy of the ball as it rises. This means that the ball does not have enough kinetic energy to reach the same maximum height it would have without air resistance.

In terms of energy conservation, the total energy of the ball (kinetic energy + potential energy) remains the same throughout its trajectory. However, the energy is redistributed as the ball moves against the force of air resistance. This is why the ball returns to its initial height with a lower speed than v(o).

Furthermore, the angle of projection does not affect the maximum height reached by the ball. This is because the only force acting on the ball is gravity, which is independent of the angle of projection. However, the velocity in the x-direction does affect the trajectory of the ball and the time it takes to reach its maximum height. This is because the velocity in the x-direction determines the horizontal displacement of the ball, while the vertical displacement is determined by the force of gravity.

In summary, air resistance plays a crucial role in the trajectory and speed of a projectile. It acts as a dissipative force and reduces the kinetic energy of the ball, resulting in a lower speed when it returns to its initial height. This phenomenon can be explained using the principles of energy conservation.