Question

consider dropping a baseball from rest at an altitude of 300 m. assume that the baseball has a drag coefficient of 0.3, a mass of 0.145 kg, and a radius of 3.7 cm. a. what is the terminal speed vᵣ of this baseball?

Answer 1

To calculate the terminal speed of the baseball, balance the gravitational force with the drag force using relevant equations and solve for the terminal velocity.

Step-by-step explanation:

Terminal Velocity of a Baseball

To calculate the terminal speed (vr) of the baseball, we use the equation for terminal velocity, which is achieved when the force of gravity is balanced by the drag force. The drag force Fd can be calculated using the equation Fd = (1/2)ρCdAv2, where ρ is the air density (approximately 1.225 kg/m3 at sea level), Cd is the drag coefficient, A is the cross-sectional area, and v is the velocity. For a spherical object, the cross-sectional area A can be found by πr2, with r being the radius of the baseball.

To find the terminal velocity we set the gravitational force equal to the drag force: mg = (1/2)ρCdAvr2. Solving for vr gives us the terminal velocity of the baseball.