A ball is thrown horizontally and at the same time another ball is dropped vertically from the top of a tower. Will both the balls strike the ground with same velocity?

No. The ball which is thrown horizontally from the top of a tower of height $H$ will attain a velocity of \[v_R^2=v_H^2+v_V^2=v_H^2+2gH\]

And, the ball which is simply dropped from the same height will attain the final velocity of \[v^2=2gH\]

Because of the factor $v_H,$ the ball thrown horizontally will strike the ground with more velocity.

[Read: Projectile Fired Horizontally from the Top of a Tower]

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