A projectile is fired at an angle of 30 degrees from the horizontal, it reaches a maximum height of 12m above the ground before coming to rest 600m from its initial starting point at the same level. What is the initial speed of the projectile?

At first glance this question seems require solving in several steps, splitting horizontal and vertical components, taking a value for time from the motion under constant acceleration and then applying this to the motion under constant velocity and determining the speed using its horizontal component. While this is a valid method there is a faster and simpler method. Firstly consider the vertical motion only, here the object is under constant acceleration due to gravity. Now we think of all the information we have about this motion and what we want to find, we want to find the initial upwards velocity and we know the vertical displacement, the final velocity and the acceleration. From this we pick out the correct equation and solve for the initial velocity. Then we can solve for the initial total speed by resolving the magnitude of that velocity into the known direction of the initial velocity at 30 degrees to the horizontal. Doing this gives us a final answer of 30.7 meters per second, a very high speed. The trick to answering this question was recognizing that the initial vertical velocity is just a component of the total initial velocity, and knowing the initial velocities direction the speed can be obtained.