Who Reaches Fastest?

The velocity of a ball in horizontal projectile motion from a height $\color{#E81990}h$ whose initial velocity is $\color{#20A900}u$ is given by the formula : $\large {\color{#3D99F6}v} = \sqrt{{\color{#20A900}u^2} + 2g{\color{#E81990}h}}$ All all the three balls have same initial velocity $({\color{#20A900}u})$ and are projected from same height $({\color{#E81990}h})$ their velocity while hitting $({\color{#3D99F6}v})$ will be the same.

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How do we get the formula for velocity ?

Let us consider a particle of mass $m$ which is being projected from a height $h$ with initial velocity $u$ . From law of conservation of energy we get, $\begin{aligned} \text{Total Energy at the top} & = \text{Kinetic Energy while hitting the ground} \\ mgh + \dfrac{1}{2}mu^2 & = \dfrac{1}{2}mv^2 \\ v^2 & = 2gh + u^2 \\ v & = \sqrt{u^2 + gh} \\ \end{aligned}$ You can see that the above relation is independent of the angle at which the particle is projected.

Use energy conservation: $U_i+ K_i= U_f+K_f$

The initial and final potential energies are the same for each ball, because they all start from the same height and end at ground level. They all have the same initial kinetic energies...so, they all must have the same final kinetic energies.

Each ball hits the ground with the same speed.

The initial angle doesn't matter! The angle affects the direction of each ball on impact, but not the speed.