Net force on ball,
F=−mg−mγv2
a=−g−γv2
dtdv=−g−γv2
∫v=V0v=0g+γv2dv=∫t=0t−dt
(gγ1tan−1gγv)v=V0v=0=−t
∴t=γg1tan−1(gγV0)
A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2 (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is:
Held on 10 Apr 2019 · Verified 6 Jul 2026.
γg1ln(1+gγV0)
γg1tan−1(gγV0)
γg1sin−1(gγV0)
2γg1tan−1(g2γV0)
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