Question

A bullet of mass m = 8.00 g is fired into a block of mass M = 150 g that is initially at rest at the edge of a table of height h = 1.00 m (see figure below). The bullet remains in the block, and after the impact the block lands d = 2.30 m from the bottom of the table. Determine the initial speed of the bullet.

___ kg/s

Answer 1

Solution.

$m=0.008kg;$

$M=0.150kg;$

$h=1.00m;$

$d=2.3m;$

$v_i-?$

$mv_i+M\sdot 0=(m+M)v_f;$

$v_i=\dfrac{(m+M)v_f}{m};$

$h=\dfrac{gt^2}{2}\implies t=\sqrt{\dfrac{2h}{g}};$

$t= \sqrt{\dfrac{2\sdot1.00}{9.8}}=0.45s;$

$d=v_f\sdot t\implies v_f=\dfrac{d}{t};$

$v_f=\dfrac{2.3}{0.45}=5.1m/s;$

$v_i=\dfrac{(0.008+0.15)\sdot5.1}{0.008}=100.725m/s;$

Answer:$100.725 m/s.$