A target in a shooting gallery consists of a vertical square wooden board. 0.230

Question

A target in a shooting gallery consists of a vertical square wooden board. 0.230 m on a side and with mass 0.730 kg, that pivots on a horizontal axis along its top edge. The board is struck face-on at its center by a bullet with mass 1.70 g that is traveling at 305 m/s and that remains embedded in the board. What maximum height above the equilibrium position does the center of the board reach before starting to swing down again? What minimum bullet speed would be required for the board to swing all the way over after impact?

Explanation / Answer

given that

mass m=0.730 kg

mass M=0.0017 kg

bullet velocity ub =305 m/s

wooden plank velocity =u=0

this problem belongs to ballistic penduium of collision

according to law of conservation of momentum

mUb +Mu = [m+M] Vmin

Part B

according to law of conervation of momentum

Vbullet = [m+M/m](2gh)^1/2

305 =[0.0017+0.73]/0.0017 (2*9.8*H)^1/2

0.709 =[2gH]^1/2

Hmax = (0.709)^2/2*9.8

=0.025 m

Part C

the bullet speed after collision

V=[m/m+M] V bullet

=[0.0017/0.0017+0.73 ] *305 =

=0.7086 m/s

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