Question

A 100g bullet is fired on a ballistic gel with a force constant of 200N/m/s. The ballistic gel is large enough to cover the trajectory of the bullet. If the initial speed of the bullet is 700m/s upon entering the ballistic gel, how long (in seconds) will it take the gel to slow the bullet to 0.01m/s? Ignore acceleration due to gravity. 

Answer 1

Solution.

$m=100g=0.1kg;$

$k=200N/(m/s);$

$v_o=700m/s;$

$v=0.01m/s;$

$t-?;$

$a=\dfrac{v-v_o}{t} \implies t=\dfrac{v-v_o}{a};$

$a=\dfrac{F}{m};$ $k=\dfrac{F}{\Delta v}\implies F=k\Delta v;$

$t=\dfrac{\Delta v m}{k\Delta v}=\dfrac{m}{k};$

$t=\dfrac{0.1kg}{200N/(m/s)}=0.0005s;$

Answer: $t=0.0005s.$