Explanation

(b) From conservation of mechanical energy
$K = K_{i} - mgy$ ….(i)
(Here $K_{i}$= initial kinetic energy = constant)
$ie,K - y\ $graph is straight line. It first decreases linearly becomes minimum at highest point and then becomes equal to $K_{i}$ in the similar manner. Therefore, $K - y$ graph should be as shown below
[image:4_image92.emf]
Eq. (i) we can written as
$K = K_{i} - mg\left( u_{y}t - \frac{1}{2}gt^{2} \right)$
$ie,K - y$ graph is a parabola. Kinetic energy first decreases and then increases.
Eq. (i) can also written as
$K = K_{i} - mg\left( xtan\ \theta - \frac{gx^{2}}{2u_{x}^{2}} \right)$
Again $K - x$ graph is a parabola
Further, $p^{2} = 2Km\ ie,\ p^{2} = 2Km\ ie,\ p^{2} = K$ or $K\ versus\ p^{2}$
Graph is a straight line passing through origin