Assertion : At any instant the magnitude of rate of change of potential energy of the projectile of mass 1 kg is numerically equal to magnitude of a v (where, a is acceleration due to gravity and v is velocity at that instant). Reason : The graph representing power delivered by the gravitational force acting on the projectile with time will be straight line with negative slope.

Step-by-step solution

( array l & Assertion d U d t = d d t (m g h)=m g d d t (u_y t- 1 2 g t^2 ) & =m g (u_y-g t )=m g v_y & | d v d t | =m g |v_y | array ) For ( aligned m & =1 ~kg | d U d t , & =g (u_y-g t ) (ii) a v & =(-g j ) [u_x i + (u_y-g t ) j ] & =g (u_y-g t ) (ii) aligned ) From Eqs. (i) and (ii), we can see that two magnitudes are equal. Reason (P= F v =(-m g i ) [v_x i + (u_y-g t ) j ] ) (=-m g u_y+m g^2 t ) So, (P ) versus t graph has the positive slope.