Explosives are used to blow a rock apart. The explosion blows the rock into thre

Question

Explosives are used to blow a rock apart. The explosion blows the rock into three fragments. Two fragments go off at a 107 degree angle to each other--a 3.9 kg piece at 24.2 m/s and a 6.2 kg piece at 21.7 m/s. Calculate the speed of the third piece, if it has a mass of 5.8 kg.

Explanation / Answer

We first have to break it into x and y components, To make it easy, we will make the 3.9 kg at 24.2 m/s along the x axis, on the negative side and the other 6.2 kg piece will be 107 degrees away from the first piece, or 73 degrees from the positive x axis We have to break down the momentum of the 6.2 piece into x component and y components momentum = (6.2)(21.7) = 134.54 x component --> cos 73 = x/134.54 x= 39.34 y component --> sin 73 = y/134.54 y= 128.66 So we find the x components combined, 39.34 - (3.9 x 24.2) = -55.04 y component is 128.66 To find the thrid piece momentum, we make the x and y components opposite signs, because momentum should be conserved So the momentum components of the 3rd piece are 55.04 and -128.66 Use pythagorean theorem to find magnitude, 139.94 Momentum = speed x mass 139.94 = v(5.8) v= 24.13 m/s

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