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.
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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