Question

A bullet of 10 grams strikes a sand bag at speed of 10^3 ms-1 and gets embedded after calculating 5 cm

Calculate :

(i) The resistive force exerted by the sand on bullet
(ii) The time taken by the bullet to come to rest
​

Answer 1

${\mathfrak{\underline{\purple{\:\:\: Given:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\sf{ Mass \: of \: bullet\:(m) = 10 \: g}$

$\:\:\:\:\bullet\:\:\:\sf{ Speed \: of \: bullet\:(u) = 10^{3} \: m/s}$

$\:\:\:\:\bullet\:\:\:\sf{ Travelled \: distance\:(s) = 5 \: cm}$

${\mathfrak{\underline{\purple{\:\:\:To \:Find:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\sf{ Force \: exerted\:(F)}$

$\:\:\:\:\bullet\:\:\:\sf{ Time \: taken\:(t) }$

${\mathfrak{\underline{\purple{\:\:\: Solution:-\:\:\:}}}}$

$\dashrightarrow\:\: \sf{ {v}^{2} = { u}^{2} + 2as}$

$\dashrightarrow\:\: \sf{ {0}^{2} = ({10}^{3} )^{2} + 2 \times a \times 0.05 }$

$\dashrightarrow\:\: \sf{ - {10}^{6} = \frac{a}{10} }$

$\dashrightarrow\:\: \sf{ - { 10}^{7} = a }$

$\dashrightarrow\:\: \sf{ a = - 10^{7} \: m/ {s}^{2} }$

$\dashrightarrow\:\: \sf{Mass = \frac{10}{1000} = 0.01 \: kg}$

$\longrightarrow\:\: \sf{F = ma}$

$\longrightarrow\:\: \sf{ F= 0.01 \times - {10}^{7} }$

$\longrightarrow\:\: \sf{ F= - 10 ^{5} \: N}$

$\therefore \:\sf{Force\: \: exerted \:\: of \:\:bullet \:\: is\: \: {10}^{5} \: N \: \:in\: \: backward\: \: direction}$

$\hookrightarrow\:\: \sf{ v = u + at }$

$\hookrightarrow\:\: \sf{ 0 = 10^{3} + ( - 10^{7} ) \times t }$

$\hookrightarrow\:\: \sf{ - 10 ^{3} = - 10^{7} \times t }$

$\hookrightarrow\:\: \sf{ t = \dfrac{ - 10^{3} }{ - {10}^{7} } }$

$\hookrightarrow\:\: \sf{ t = \dfrac{1}{10^{4} } \: sec}$

$\therefore\:\sf{ The\:\:time \:\: taken \:\: is \:\: {10}^{ - 4} \:\: seconds}$