Question

A particle moves on a given straight line with a constant speed v. At a certain time it is at a point P on its straight line path. O is a fixed point. Show that OP x v is independent of the position P.

Answer 1

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ANSWER::

For better understanding see the figure.

The particle moves on the straight line PP' at speed v.

According to the figure,

OP x v = (OP) v sinФ n = v(OP) sinФ n = v(OQ) n

So, we can see that from the figure,

OQ = OP sin Ф = OP' sin Ф'

So, the magnitude of OP x v remain constant irrespective of the position of the particle.

Therefore , OP x v is independent of position P.

Hope it helps!