When dealing with the motion of an object in 2 dimensions, also called projectile motion, we take advantage of one fascinating feature of vectors- components! Recall that a vector has direction and magnitude; this means that the vector has a length (magnitude) and is at an angle with “something else” (direction). We normally use the ground as that “something else” to measure angle. We can separate a vector into two new vectors (called components) by using some ingenious geometry:

vector into two new vectors (called components) by using some ingenious geometry:

Once we have our components, we can significantly simplify our situation. The vectors we care about in this case are position, velocity, and acceleration.

Distinct Dimensions:

By separating the vectors into components, we can consider motion along those vectors separately. The motion along x alone won’t depend on the motion along y alone, and vice versa. Once we have our components, we can use the usual 1-D kinematic equations for the two components separately:

In the x-direction:

and in the y-direction:

It is very important to keep the x and y components separate while you are calculating the motion. If your final answer must be in terms of a net vector, you can use the same trigonometry above to solve for the magnitudes and directions of your final vectors.

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