To find the height of an object thrown straight up with an initial velocity of 30 m/s, energy conservation principles can be applied. The kinetic energy (KE) at launch is converted into potential energy (PE) at the peak height, leading to the equation 1/2 mv^2 = mgh. Simplifying this gives 1/2 (30)^2 = 9.8h, allowing for the calculation of height. Alternatively, the equations of motion can be used, where the final velocity (v) at the peak is 0, and the initial velocity (u) is 30 m/s. Both methods effectively demonstrate how to determine the maximum height reached by the object.