Question

A baseball player hits the ball and then runs down the first base line at 22 ft/s. The first baseman fields the ball and then runs toward first base along the second base line.

Answer 1

To determine the work done by air resistance on a baseball, we calculate the change in its kinetic and potential energy based on its initial and final speeds, mass, distance traveled, and changes in height, and then subtract the work done by gravity.

Step-by-step explanation:

Finding the Work Done by Air Resistance on a Baseball

The problem is asking to find how much work is done on a baseball by air resistance given its mass, initial speed, final speed, horizontal displacement, and change in height. To calculate this, we need to consider the work-energy principle which states that the work done by all forces acting on an object equals the change in its kinetic energy plus the work done against gravity (potential energy change).

Firstly, we calculate the kinetic energy at the beginning (K₁) and at the end (K₂) using the formula K = 1/2 m v², where m is mass and v is speed. Then we calculate the change in potential energy (U) caused by the height difference using U = mgh, where g is the acceleration due to gravity (9.8 m/s²) and h is the change in height.

The work done by air resistance (Wᴇ) is the difference between the total work (which is the change in kinetic energy plus potential energy change) and the work done by gravity alone, i.e., Wᴇ = ΔK + U (work done against gravity). By substituting the given values into these equations, we can find the work done by air resistance.