Calculation:
Given,
Initial velocity of the ball,
u=V0 Drag force,
Fd=myv2 Velocity at a maximum height
=0 Where
m is the Mass of the ball,
v is its instantaneous velocity
and
y is a constant
We know that acceleration is the change in velocity.
Force is given by,
F=ma Thus, the net force on the ball:
Fnet=mg+myv2 F‌net ‌=m(g+yv2) Acceleration is given by,
a=‌ a=‌ a=−(g+yv2) Thus, net acceleration is the change in the velocity,
‌=a ‌=−(g+γv2) ‌=dt ‌=dt Integrating both the sides,
v‌=dt Let time
t required to rise to its zenith
(v=0) so,
⇒‌‌0‌=dt We know that, according to integral formula,
∫‌dx=‌tan−1(‌)+C Thus,
⇒‌‌0‌=dt Here,
x=√‌,a=v ⇒t=‌{[−‌tan−1(‌)]V00+C} [ for
Hmax,v=0] t=0−‌(−√‌tan−1(‌)) ⇒t=‌tan−1(‌) Therefore, the time taken by the ball to rise to its zenith is
‌tan−1(√‌V0)