Question # A particle moves along the straight line ( y=D ). The speed of the particle is ( v mathrm{m} / mathrm{s} ) towards right then

# A particle moves along the straight line ( y=D ). The speed of the particle is ( v mathrm{m} / mathrm{s} ) towards right then

find ( frac{d theta}{d t} )

(1) ( frac{v}{D tan theta} )

(2) ( frac{v}{D} cos ^{2} theta )

(3) ( frac{v}{D} )

(4) ( frac{V}{sec ^{2} theta} )

Solution

( tan theta=frac{x}{D} Rightarrow x=D tan theta )

( quad frac{d x}{d t}=v )

( Rightarrow frac{d x}{d t}=frac{d}{d t}(D tan theta) )

( Rightarrow quad V=D sec ^{2} theta frac{d theta}{d t} )

( Rightarrow frac{d theta}{d t}=frac{v}{D sec ^{2} theta}=frac{v}{D} cos ^{2} theta )

( quad ) option (2)