To find the velocity of an object launched at a 45-degree angle using only mass and distance, the mass is irrelevant if only gravity is acting on the object. The formula S = V^2/g can be derived from basic motion laws, where S is the distance traveled and g is gravitational acceleration, applicable specifically for a 45-degree launch. A diagram of the projectile's trajectory can help visualize the problem, focusing on the maximum height for vertical displacement and corresponding horizontal displacement. The discussion also highlights curiosity about practical applications, such as calculating velocity in a potato launcher scenario. Understanding these principles can aid in solving similar projectile motion problems effectively.