Answer:
a) The bullet will penetrate 0.375 meters into the bag of sand.
b) The average force exerted by the sand is 15 newtons.
Explanation:
The statement is incorrectly written. The correct form is presented below:
<em>A bullet of mass 50 grams travelling with a speed of 15 meters per second penetrates into a bag of sand and is uniformly brought to rest in 0.05 second.</em>
<em>a)</em><em> How far the bullet will penetrate into the bag of sand?</em>
<em>b)</em><em> The average force exerted by the sand?</em>
b) The average force exerted by the sand on the bullet (
), measured in newtons, is determined by Principle of Linear Momentum Conservation and Impulse Theorem:
(1)
Where:
- Mass of the bullet, measured in kilograms.
,
- Initial and final speeds of the bullet, measured in meter per second.
- Impact time, measured in seconds.
If we know that
,
,
and
, then the average force exerted by the sand is:


The average force exerted by the sand is 15 newtons.
a) The distance travelled by the bullet (
), measured in meters, is determined by application of Principle of Energy Conservation and Work-Energy Theorem:
(2)
If we know that
,
,
and
, then the distance travelled by the bullet is:
![\Delta s = \frac{(0.05\,kg)\cdot \left[\left(0\,\frac{m}{s} \right)^{2}-\left(15\,\frac{m}{s} \right)^{2}\right]}{2\cdot (-15\,N)}](https://tex.z-dn.net/?f=%5CDelta%20s%20%3D%20%5Cfrac%7B%280.05%5C%2Ckg%29%5Ccdot%20%5Cleft%5B%5Cleft%280%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D-%5Cleft%2815%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D%5Cright%5D%7D%7B2%5Ccdot%20%28-15%5C%2CN%29%7D)

The bullet will penetrate 0.375 meters into the bag of sand.