A ball falls from a tall bridge. The ball has a mass of 0.15 kg. The air density is 1.225 kg/m3
. The ball’s surface area is 0.0026 m2
. The ball’s coefficient of drag is 0.007. What is the ball’s terminal velocity?(1 point)
To find the ball's terminal velocity, we need to consider the forces acting on the ball as it falls. The two main forces are gravity (weight) pulling the ball down and air resistance (drag) pushing against it.
The weight of the ball can be calculated using the formula:
Weight = mass x gravity
Weight = 0.15 kg x 9.81 m/s^2
Weight = 1.4715 N
The drag force can be calculated using the formula:
Drag force = 0.5 x air density x velocity^2 x surface area x coefficient of drag
Drag force = 0.5 x 1.225 kg/m^3 x velocity^2 x 0.0026 m^2 x 0.007
At terminal velocity, the drag force equals the weight of the ball:
1.4715 N = 0.5 x 1.225 kg/m^3 x velocity^2 x 0.0026 m^2 x 0.007
Solving for velocity:
velocity^2 = (1.4715 N) / (0.5 x 1.225 kg/m^3 x 0.0026 m^2 x 0.007)
velocity = √((1.4715 N) / (0.5 x 1.225 kg/m^3 x 0.0026 m^2 x 0.007))
Calculating this out gives a terminal velocity of approximately 20.18 m/s.