In a ballistics demonstration a police officer fires a bullet of mass $50.0 \;g$ with speed $200 \;m s ^{-1}$ on soft plywood of thickness $2.00 \;cm .$ The bullet emerges with only $10 \%$ of its initial kinetic energy. What is the emergent speed of the bullet?
In a ballistics demonstration a police officer fires a bullet of mass $50.0 \;g$ with speed $200 \;m s ^{-1}$ on soft plywood of thickness $2.00 \;cm .$ The bullet emerges with only $10 \%$ of its initial kinetic energy. What is the emergent speed of the bullet?
Answer The initial kinetic energy of the bullet is $m v^{2} / 2=1000 J .$ It has a final kinetic energy of $0.1 \times 1000=100 J$. If $v_{f}$ is the emergent speed of the bullet.
$\frac{1}{2} m v_{f}^{2}=100 J$
$v_{f}=\sqrt{\frac{2 \times 100 J }{0.05 kg }}$
$=63.2 m s ^{-1}$
The speed is reduced by approximately $68 \%$ (not $90 \%)$
Similar Questions
A boy is rolling a $0.5\, kg$ ball on the frictionless floor with the speed of $20\, ms ^{-1}$. The ball gets deflected by an obstacle on the way. After deflection it moves with $5 \%$ of its initial kinetic energy. What is the speed of the ball now ? (in $ms ^{-1}$)
A boy is rolling a $0.5\, kg$ ball on the frictionless floor with the speed of $20\, ms ^{-1}$. The ball gets deflected by an obstacle on the way. After deflection it moves with $5 \%$ of its initial kinetic energy. What is the speed of the ball now ? (in $ms ^{-1}$)
- [JEE MAIN 2021]
$A$ box of mass $m$ is released from rest at position $1$ on the frictionless curved track shown. It slides a distance $d$ along the track in time $t$ to reach position $2$, dropping a vertical distance $h$. Let $v$ and $a$ be the instantaneous speed and instantaneous acceleration, respectively, of the box at position $2$. Which of the following equations is valid for this situation?
$A$ box of mass $m$ is released from rest at position $1$ on the frictionless curved track shown. It slides a distance $d$ along the track in time $t$ to reach position $2$, dropping a vertical distance $h$. Let $v$ and $a$ be the instantaneous speed and instantaneous acceleration, respectively, of the box at position $2$. Which of the following equations is valid for this situation?
A ball is dropped from a height of $20\, cm$. Ball rebounds to a height of $10\, cm$. What is the loss of energy ? ................ $\%$
A ball is dropped from a height of $20\, cm$. Ball rebounds to a height of $10\, cm$. What is the loss of energy ? ................ $\%$
Find the speed of a body at the ground when it fall freely at height $2\,m$. $(g = 10\, ms^{-2})$
Find the speed of a body at the ground when it fall freely at height $2\,m$. $(g = 10\, ms^{-2})$
Aball of mass $m$ is released from Ainside $a$ smooth wedge of mass $m$ as shown in the figure. What is the speed of the wedge when the ball reaches point $B$ ?
Aball of mass $m$ is released from Ainside $a$ smooth wedge of mass $m$ as shown in the figure. What is the speed of the wedge when the ball reaches point $B$ ?