Answer:
Option A
Explanation:
Given , velocity of the ball , v=$ (20 \hat{i}+24\hat{j})$ m/s and mass of the ball, m=2kg
From the equation of motion , when a ball is thrown,
v=u-gt .........(i)
Substituting the given values in Eq.(i) , we get
v= $ (20 \hat{i} +24 \hat{j})-(10 \hat{j})8$
= $20 \hat{i}+24 \hat{j}-80 \hat {j}= 20 \hat{i}-56 \hat{j}$ .....(ii)
From the law of conservation of energy , change in potential energy of the ball= change in kinetic energy of the ball
$\Rightarrow$ $\triangle PE$= $\frac{1}{2}mu^{2}-\frac{1}{2}mv^{2}$
= $\frac{1}{2}m(u^{2}-v^{2})$
$=\frac{2}{2}(u.u-v.v)$
=$[(20 \hat{i}+24 \hat{j}).(20 \hat{i}+24 \hat{j})- [(20 \hat{i}-56 \hat{j}).(20 \hat{i}-56 \hat{j})]$
= $ (20)^{2}+(24)^{2}-(20)^{2}-(56)^{2}$
= $(24)^{2}-(56)^{2}$= 576-3136
=-2560=-2.56 kJ
