To determine how fast Josh will be going at the bottom of the hill, we apply the principle of conservation of mechanical energy. The potential energy at the top of the hill is converted into kinetic energy at the bottom. The equation used is: (1/2) m v_f^2 + m g h = (1/2) m v_i^2, where m is mass, v_i is initial velocity (10 m/s), v_f is final velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the hill (30 m). By substituting the known values and solving for v_f, we find that v_f is approximately 37 m/s. This means that Josh will be traveling at a speed of about 37 m/s when he reaches the bottom of the hill.