Final answer:
To determine the time at which a particle reaches its highest point in projectile motion, we can use the kinematic equation 0 = Voy - gt, solving for t to find t = Voy/g, where Voy is the initial vertical velocity and g is the acceleration due to gravity.
Step-by-step explanation:
To find the time at which a particle is at its highest point, we use kinematics equations for projectile motion. At the highest point, the vertical component of the velocity (Vy) will be zero because the particle is momentarily not moving up or down. This is the point where all the vertical kinetic energy has been converted into gravitational potential energy. The relevant kinematic equation is 0 = Voy - gt, where Voy is the initial vertical velocity and g is the acceleration due to gravity (approximately 9.81 m/s2 on Earth, downward). Solving this equation for t will give the time at which the particle's vertical velocity is zero, and thus at its highest point. To solve for t, we rearrange the equation to t = Voy/g. This result shows that the time to reach the highest point is directly proportional to the initial vertical velocity and inversely proportional to the gravitational acceleration.