A spot of light S rotates in a horizontal plane with a constant angular velocity of 0.1 rad / s . The spot of light P moves along the wall at a distance of 3 m from S . The velocity of spot P , where =45^ , is

Step-by-step solution

The situation is shown in figure. From figure, x=r Velocity of P is v= d x d t =r ^2 ( d d t ) where, d d t = angular velocity of rotation of spot aligned & = & v= r ^2 & At =45^ , & so =45^ & Hence, aligned & v & =0.1 3 ^2 45^ & = & 0.1 3 2=0.6 ~m / s aligned aligned