Here\'s the question. A container explodes and breaks into three fragments that
ID: 1983180 • Letter: H
Question
Here's the question. A container explodes and breaks into three fragments that fly off 120 degrees apart from each other, with mass ratios of 1:4:2. If the first piece flies off with a speed of 6.0m/s, what is the speed of the other two fragments?
Explanation / Answer
............mass = 4m, vel = v2 ..............* ..............* ..............| --------------*-------------------> ..........*.......*...30 degree .....*...............*....... *.........................* mass = m, mass = 2m Vel = v1=6 m/sec, vel = v3 Consider the diagram above, before the explosion the total system momentum is zero. Upon explosion the object will break in to three fragments. The vector sum of the momentum of three individual fragments remains the zero (conservation of momentum) Break the momentum of mass 2m in positive x and negative y direction as 2m* v3 cos 30 and 2m* v3 sin30, similarly break the momentum of mass m in to negative x and negative y direction as m*v1 cos 30 and m*v1 sin 30 Now equate these vector in x and y directions as 4m*v2 = m*v1 sin 30 + 2m* v3 sin 30 ----------- in y direction and which is 4v2 = v1*(1/2) + 2v3*(1/2) 4v2 = (v1)/2 + v3 -------------1) 2m* v3 cos 30 = m*v1 cos 30 ---------------------2) in x direction 2v3 = v1 = 6m/sec v3 = 3 m/sec from equation 1) 4 v2 = 6/2 + 3 = 6 v 2 = 6/4 = 3/2 m/sec Hence velocity of mass 4m would be 3/2 m/sec and velocity of mass 2m would be 3m/sec The direction will depends on the assumption of direction of 1st fragment.