A ball of mass 50 is thrown vertically upwards with an initial velocity of 20 ms^(1) Calculate: (i) in the initial kinetic energy imparted to the ball, (ii) the maximum height reached if air friction is neglected, and (iii) the maximum height reached if 40% of the initial energy is lost against the air friction.Take g=10 ms^(-2)

A ball of mass 50 is thrown vertically upwards with an initial veloci

1.	A ball of mass 50 is thrown vertically upwards with an initial velocity of 20 ms^(1) Calculate: (i) in the initial kinetic energy imparted to the ball, (ii) the maximum height reached if air friction is neglected, and (iii) the maximum height reached if 40% of the initial energy is lost against the air friction.Take g=10 ms^(-2)
Answer» Solution :GIVEN :m =50g=`(50)/(1000)` kg =0.05 kg u=20 m `s^(-1)` ,g=10 m `s^(-2)` (i)Initial kinetic energy imparted to the ball `=(1)/(2)mu^(2)=(1)/(2)xx0.05xx(20)^(2)=10J` (ii)If AIR friction is negligible ,then POTENTIAL energy at the maximum height or mgh =`(1)/(2)mv^(2)` `therefore H=(v^(2))/(2g)=((20)^(2))/(2xx10)=20 m` (iii)If 40 % of the initial energy is lost against the air friction .then Potential energy at the maximum height 60)/(100)xx"initial kinetic energy"` or `mgh=(60)/(100)xx(1)/(2)mv^(2)` `therefore h=(0.6 v^(2))/(2g)=(0.6xx(20)^(2))/(2xx10)=12 m`