A bullet of mass 50 g moving at 400 mcdot s^(-1) penetrates a wall with an average force of 4xx 10 ^(4) N. Itcomes out of the other side of the wall at 50 mcdot s^(-1). Find the thickness of the wall.

A bullet of mass 50 g moving at 400 mcdot s^(-1) penetrates a wall wit

1.	A bullet of mass 50 g moving at 400 mcdot s^(-1) penetrates a wall with an average force of 4xx 10 ^(4) N. Itcomes out of the other side of the wall at 50 mcdot s^(-1). Find the thickness of the wall.
Answer» Solution :In the case of the 1st bullet, m = 50 g = 5 `xx 10^(-3)` kg As the average force = `4 xx 10^(4)`N, a = average retardation = `(4 xx 10^(4))/(50 xx 10^(-3)) "m"cdot s^(-2)` u = initial velocity = 400 m`cdot s^(-1)` V = final velocity = 50 m`cdot s^(-1)` Let the thickness of the WALL = s. From`v^(2) = u^(2) - 2`as. s = `(u^(2) - v^(2))/(2a) = ((400^(2) - 50^(2)) xx 50 xx 10^(-3))/(2 xx 4 xx 10^(4)) = 0.0984`m The second bullet cannot penetrate the wall, hence its final velocity should be 0, i.e.,v = 0. As it cannot cover the distance s , the maximum possible mass `m_(0)` corresponds to s = 0.0984 m. Average retardation, a = `(F)/(m_(0)) = (u^(2) - v^(2))/(2s) = (u^(2))/(2s)` or,`m_(0) = (2Fs)/(u^(2)) = (2 xx 4 xx 10^(4) xx 0.0984)/(400^(2)) = 0.0492` kg