To solve the projectile motion problem, the key equations involve breaking down the initial velocity into horizontal and vertical components using trigonometric functions. The horizontal displacement can be calculated using the formula distance = velocity × time, while vertical displacement requires the use of kinematic equations for free-falling bodies. The time of flight can be determined by analyzing the vertical motion and applying the appropriate equations. Understanding the relationship between the angle of launch and the components of velocity is crucial for solving these types of problems. Trigonometry plays a significant role in finding the initial velocity and other parameters needed for the calculations.