Terminal Velocity Calculator

Terminal Velocity Calculator:

Enter the values of mass m_(kg),  acceleration due to gravity g_(m/s2),  density of the fluid ρ_(kg/m3), cross-sectional area A_(m2), drag coefficient C_d, to determine the value of terminal velocity V_t(m/s).

Enter Mass :		kg
Enter Acceleration Due to Gravity :		m/s2
Enter Density of the Fluid :		kg/m3
Enter Cross-Sectional Area :		m2
Enter Drag Coefficient :		d
Result – Terminal Velocity :		m/s

Terminal Velocity Formula:

Terminal velocity is defined as the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration.

Terminal velocity, V_t(m/s) in metres per second is equated by the square root of the product of two times of mass of the object, m_(kg) in kilograms, acceleration due to gravity, g_(m/s2) in metres per second squared and then divided by the product of density of the fluid, ρ_(kg/m3) in kilogram per cubic metres, area of the cross-section, A_(m2) in metre squared and drag coefficient, C_d.

Terminal velocity, V_t(m/s) = √( 2 * m_(kg)* g_(m/s2)/ ρ_(kg/m3)* A_(m2)* C_d)

V_t(m/s) = terminal velocity in metres per second, m/s.

m_(kg) = mass in kilograms, kg.

g_(m/s2) = acceleration due to gravity in metres per second squared, m/s².

ρ_(kg/m3) = density of the fluid in kilograms per cubic metres, kg/m³.

A_(m2) = cross-sectional area in metre squared, m².

C_d = drag coefficient.

Terminal Velocity Calculation:

1.A baseball with a mass of 0.145 kg falls through the air where the density is 1.225 kg/m³. Assume the cross-sectional area of the baseball is 0.0042 m² and the drag coefficient is 0.5. Find the terminal velocity of the baseball.

Given: m_(kg) = 0.145kg, g_(m/s2) = 9.81m/s², ρ_(kg/m3) = 1.225kg/m³, A_(m2) = 0.0042m²,

C_d = 0.5.

Terminal velocity, V_t(m/s) = √( 2 * m_(kg)* g_(m/s2)/ ρ_(kg/m3)* A_(m2)* C_d)

V_t(m/s) = √( 2 * 0.145 * 9.81 / 1.225 * 0.0042 * 0.5)

V_t(m/s) = √( 1104.82)

V_t(m/s) = 33.25m/s.

2.A skydiver with a mass of 70 kg falls through the air where the density is 1.225 kg/m³. Assume the cross-sectional area of the skydiver is 0.7 m² and the terminal velocity is 40.02m/s. Calculate the drag coefficient.

Given: m_(kg) = 70kg, g_(m/s2) = 9.81m/s², ρ_(kg/m3) = 1.225kg/m³, A_(m2) = 0.7m²,

V_t(m/s) = 40.02m/s.

Terminal velocity, V_t(m/s) = √( 2 * m_(kg)* g_(m/s2)/ ρ_(kg/m3)* A_(m2)* C_d)

C_d = 2 * m_(kg)* g_(m/s2)/ ρ_(kg/m3)* A_(m2)* V²_t(m/s)

C_d = 2 * 70 * 9.81 / 1.225 * 0.7 * 40.02²

C_d = 1.