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The velocity, , of an object that falls freely due to the Earth gravity can be modeled with the equation: m dv/dt = -mg + kv^2
where m is the mass of the object, g = 9.81 m/s^2, and k is a constant. Solve the equation for v for the case that m = 5 kg, k = 0.05 kg/m, 0

Answer :

V=√1962 tan h (-√1962t/100) is the velocity of the object that is falling freely due to earth's gravity.

What is Newton second law of motion?

The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

According to Newton's second law of motion,

mdv/dt= -mg+kv²

Calculation:

mdv/dt=-mg+kv²

5dv/dt=-10g+0.05v²

dv/dt=-2×9.81×0.01v²

dev/dt=0.01v²-19.62

-1/19.62 dv/dt =1-v²/1962

-1/19.62 ∫dv/1-v²/1962=∫dt

√1962 Tanh∧-1 (v/√1962)=-19.62t

Tanh∧-1(v/√1962)=-√1962/100 t

v=√1962 Tan h∧-1 (-√1962t/100)

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