In a typical two-dimensional projectile motion problem we simply say that it is too complicated to solve the problem by considering the (typically) parabolic path the object follows.

Instead, because the X and Y motions are independent of one another, we break the problem down into two separate sub-problems.

The X sub-problem is a one-dimensional motion problem (this is often a constant-velocity situation).

The Y sub-problem is a separate one-dimensional motion problem (this is often a constant-acceleration situation).

You know how to solve 1-D motion problems!

The two sub-problems are entirely independent except that the time is the same for both sub-problems.

To begin your analysis of any two-dimensional motion situation you should:

• Draw a diagram of the situation.
• Draw a free-body diagram showing all forces acting on the object while it is in motion - you can refer back to this to determine the object's acceleration.
• Choose an origin.
• Choose a coordinate system (i.e., show which way is positive for your two coordinate axes).
• Organize your data, keeping the data for the X sub-problem separate from the data for the Y sub-problem.

Only when you've done all this should you turn to the constant-acceleration equations (assuming the acceleration is constant!).

In many cases you can answer a question based solely on one of the sub-problems. For instance, analyzing the Y sub-problem above gives you the answer to questions like "How long was the ball in flight?" or "What is the maximum height reached by the ball in its motion?"

In some cases you need to combine information from the two sub-problems to answer a question. An example would be "What is the speed of the object just before impact?"