A 1.0kg bomb explodes into three pieces, A, B, and C. After the
explosion piece A (300g) travels along the positive x-axis with a
speed of 300m/s. Piece B (500g) travels along the negative y-axis
with a speed of 400m/s. Find the velocity of piece C.
here,
mass A , mA = 300 g has final speed , vA = 300 i m/s
mass B , mB = 500 g has final speed , vB = - 400 j m/s
mass C , mC = 1000 g - mA - mB
mC = 200 g
let the final velocity of C be vC
using conservation of momentum
0 = mA * vA + mB * vB + mC * cC
0 = 300 * 300 i - 500 * 400 j + 200 * vC
vC = - 450 i m/s + 1000 j m/s
the magnitude of velocity , |vC| = sqrt(450^2 + 1000^2) = 1096.6 m/s
direction , theta = arctan(1000 /(-450)) = 114.23 degree counterclockwise from +x axis
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