A particle is uncharged and is thrown vertically upward from ground level with a

Question

A particle is uncharged and is thrown vertically upward from ground level with a speed of 26.1 m/s. As a result, it attains a maximum height h. The particle is then given a positive charge +q and reaches the same maximum height h when thrown vertically upward with a speed of 28.2 m/s. The electric potential at the height h exceeds the electric potential at ground level. Finally, the particle is given a negative charge -q. Ignoring air resistance, determine the speed with which the negatively charged particle must be thrown vertically upward, so that it attains exactly the maximum height h. In all three situations, be sure to include the effect of gravity.
1_________m/s

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Explanation / Answer

Let v0 = 25 m/s, v1 = 30 m/s, and v2 be the velocity of the -charge.
The +charge loses energy due to the presence of an electric field and the -charge gains the same amount of energy from the same cause.
The energy loss of the +charge = (m/2)(v1^2-v0^2)

and the energy gain of the -charge = (m/2)(v0^2-v2^2).
Thus v0^2-v2^2 = v1^2-v0^2 ==> v2^2 = 2v0^2-v1^2 ==> v2 = sqrt(2v0^2-v1^2) = 18.70829 m/s.

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