A bullet of mass m = 8.00 g is fired into a block of mass M = 280 g that is init

Question

A bullet of mass m = 8.00 g is fired into a block of mass M = 280 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 = 2.10 m from the bottom of the table. Determine the initial speed of the bullet.
m/s

A bullet of mass m = 8.00 g is fired into a block of mass M = 280 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 = 2.10 m from the bottom of the table. Determine the initial speed of the bullet.

Explanation / Answer

a) d = V*sqrt(2h/g)

2.1 = V*sqrt(2*1/9.8)

V = 4.65 m/s

according to law of conservation of momentum

m*v = ( M+m)*V

v = (M+m)*V/m = 0.288*4.65/0.008 = 167.4 m/s

b) m1*g*h1 =(m1+m2)*g*h2

h2 = 68.1*4.3/(68.1+55) = 2.378 m

c) m1*v1+m2*v2 = m1*v1'+m2*v2'

300*(-2.5) + 22.5*36.5 = 0+22.5*v2'

v2' = 3.167 m/s

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