Answer
$v_a = v_b = v_c$
Work Step by Step
Let's consider ball a. We can use conservation of energy to find the speed of the ball $v_f$ when the ball reaches the line. Let $h$ be the height of the line.
$PE_f+KE_f = PE_0+KE_0$
$mgh+\frac{1}{2}mv_f^2 = 0+\frac{1}{2}mv_0^2$
$\frac{1}{2}mv_f^2 = \frac{1}{2}mv_0^2-mgh$
$v_f^2 = v_0^2-2gh$
$v_f = \sqrt{v_0^2-2gh}$
We can use the same method to find the speed of ball b and ball c when they reach the line. Since the equation is exactly the same for all three balls, the speed of all three balls will be the same when they reach the line.
Therefore;
$v_a = v_b = v_c$
