A ball falls from a tall bridge. The ball has a mass of 0.15 kg. The air density is 1.225 kg/m^3. The ball's surface area is 0.0026 m^2. The ball's coefficient of drag is 0.007. What is the ball's terminal velocity?
a. 402 m/s
b. 30.4 m/s
c. 363 m/s
d. 164 m/s
To find the ball's terminal velocity, we can use the formula:
terminal velocity = sqrt((2 * mass * acceleration due to gravity) / (density * surface area * coefficient of drag))
Given:
Mass = 0.15 kg
Air density = 1.225 kg/m^3
Surface area = 0.0026 m^2
Coefficient of drag = 0.007
Acceleration due to gravity = 9.8 m/s^2 (approx.)
Plugging in the values:
terminal velocity = sqrt((2 * 0.15 * 9.8) / (1.225 * 0.0026 * 0.007))
= sqrt(2.94 / 0.000021455)
= sqrt(137095.148)
≈ 370.13 m/s
The ball's terminal velocity is approximately 370.13 m/s, which is closest to option c. 363 m/s.