Relative Motion in Two Dimensions
These concepts can be extended to two-dimensional spaces also. Given in the figure below, consider a particle P and reference frames S and S’. The position of the frame S’ as measured in S is rS’S, the position of the particle P as measured with respect to the frame S’ is given by rPS’ and the position of the particle P with respect to the frame of reference S is given by rPS,
Notice from the figure that,
rPS = rPS’ + rS’S
These vectors give us the formula for relative velocities too, differentiating the above equation,
⇒
Intuitively speaking, the velocity of a particle with respect to S is equal to the velocity of S’ with respect to S plus the velocity of the particle with respect to S.
Differentiating this equation again, the equation for the acceleration is given by,
⇒
The acceleration of a particle with respect to S is equal to the acceleration of S’ with respect to S plus the acceleration of the particle with respect to S.
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Relative Motion in Two Dimension
The motion of the bodies is not absolute or isolated. It is always described with respect to some reference. For example, the speed of a moving vehicle is measured with respect to the ground. The position is also measured with respect to a reference which is called the origin. A train moving has a velocity of 100 Km/h with respect to the ground, but if another train is moving at 150 km/h. The velocity of the first train will not be 100 km/h with respect to the person sitting on the second train. It is essential to study the relative motion of the objects. Let’s explore this concept in detail.
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