Question

Explosives are used to blow a rock apart. The explosion blows the rock into three fragments. Two fragments go off at a 102 degree angle to each other--a 5.8 kg piece at 28.9 m/s and a 4.9 kg piece at 30.4 m/s. Calculate the speed of the third piece, if it has a mass of 3.6 kg. 55.49 m/s

Answer 1

The speed of the third fragment is 68.4 m/s.

Resultant momentum of the two fragments

The resultant momentum of the two fragments at the given angle is calculated as follows;

$P_3^2 = P_1^2 + P_2 - 2P_1P_2 cos(102)\\\\P_3^2 = (5.8 \times 28.9)^2 + (4.9 \times 30.4)^2 \ - \ 2(5.8\times 28.9)(4.9 \times 30.4)\times cos(102)\\\\P_3^2 = 50285.55 \ + \ 10382.55\\\\P_3^2 = 60668.1\\\\P_3 = \sqrt{60668.1} \\\\P_3 = 246.31 \ kgm/s$

Speed of the third fragment

The speed of the third fragment is calculated as follows;

P = mv

$v = \frac{P}{m} \\\\v = \frac{246.31}{3.6} \\\\v = 68.4 \ m/s$

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