Question

A bullet of mass $0.2kg$, moving with a velocity of $200\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$, strikes a stationary wooden target of mass $5kg$.. If all the energy is transferred to the wooden target, calculate the velocity with which the target moves in the forward direction.

Answer 1

Step 1: Given data:

For bullet:

mass=$0.2kg$

velocity=$200\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

For wooden target:

mass=$5kg$

Let the velocity of the target be ‘v’

Formula used: $Kineticenergy=\frac{1}{2}\times mass\times {\left(velocity\right)}^2$

Step 2: To find the Kinetic energy of a bullet:

${K.E.}_{Bullet}=\frac{1}{2}\times 0.2\times {200}^2$

${K.E.}_{Bullet}=4000J$

Step 3: To find the final velocity of a wooden target:

${K.E.}_{WoodenTarget}=\frac{1}{2}\times 5\times v^2$

Kinetic energy of a wooden target = Kinetic energy of a bullet

$\frac{1}{2}\times 5\times v^2$ $=4000J$

$v^2=\frac{4000\times 2}{5}$

$v^2=1600$

$v=40\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Thus, the final velocity with which the target moves in the forward direction is $40\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$.