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CAF123 said:vel. of ball relative to earth: u + vo. Do I have to consider the velocity of the hand? The problem statement says the hand stays fixed.
Mans acceleration rel. to earth: a
Balls acceleration rel. to Earth = ##\frac{d}{dt} \left(u(t) + v_o \right)##, but I think the hand stays stationary, so acc. rel. to Earth =## \dot{u}##
Yes. You have to consider the initial velocity of the hand relative to the Earth (at time t = 0). Relative to the earth, the initial velocity of the hand is v0.
You got the man's acceleration relative to the Earth correct. But, the ball's acceleration relative to the Earth is minus g.
Are you familiar with the equation [itex]x=x_0+v_0t+\frac{1}{2}at^2[/itex]?
Now all you have to do is write the corresponding equation for the location of the ball relative to the earth.