## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

$v_a = v_b = v_c$
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 ground. $PE_f+KE_f = PE_0+KE_0$ $0+\frac{1}{2}mv_f^2 = mgh+\frac{1}{2}mv_0^2$ $v_f^2 = 2gh+v_0^2$ $v_f = \sqrt{2gh+v_0^2}$ We can use the same method to find the speed of ball b and ball c when they reach the ground. 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 ground. Therefore; $v_a = v_b = v_c$