Calculate the terminal velocity for a baseball. A baseball's diameter is approximately d = 0.073 m, and its mass is m = 0.146 kg. Express your answer in meters per second and miles per hour. (Assume a drag coefficient of 1 and air density of 1.3 kg/m3.)
__ m/s
__ mph
M g = (1/2) * (density) V^2 * Area * Cd
They tell you to assume the drag coefficient (Cd) is 1.
Compute the baseball's area and solve the above equation for V.
Then convert m/s to miles per hour.
We will be glad to critique your work
To calculate the terminal velocity of a baseball, we need to find the equilibrium between the gravitational force pulling the baseball downwards and the drag force resisting its motion through the air.
The drag force can be calculated using the formula:
Drag force = (1/2) * drag coefficient * air density * velocity^2 * projected area
Where:
- Drag coefficient is a dimensionless quantity that depends on the shape of the object and the flow characteristics of the fluid.
- Air density is the density of air, which is approximately 1.3 kg/m3.
- Velocity is the velocity of the object relative to the air.
- Projected area is the cross-sectional area of the object facing the direction of motion.
In this case, the projected area of the baseball is the same as the area of a circle with a diameter of 0.073 m.
Now, let's solve for the terminal velocity:
At terminal velocity, the drag force is equal to the gravitational force:
Drag force = gravitational force
Therefore,
(1/2) * drag coefficient * air density * velocity^2 * projected area = mass * gravitational acceleration
Substituting the given values:
(1/2) * 1 * 1.3 kg/m3 * velocity^2 * (π * (0.073/2)^2) = 0.146 kg * 9.8 m/s^2
Simplifying the equation:
0.133225 * velocity^2 = 1.4312
Solving for velocity:
velocity^2 = 1.4312 / 0.133225
velocity^2 = 10.748
velocity = √10.748
velocity ≈ 3.28 m/s
Therefore, the terminal velocity of the baseball is approximately 3.28 m/s.
To convert this into miles per hour, we can use the conversion factor:
1 m/s ≈ 2.237 mph
So, to find the terminal velocity in miles per hour:
terminal velocity ≈ 3.28 m/s * 2.237 mph/m
terminal velocity ≈ 7.33 mph
Therefore, the terminal velocity of the baseball is approximately 3.28 m/s or 7.33 mph.