A 32.0-kg body is moving in the direction of the positive x axis with a speed of
ID: 1778116 • Letter: A
Question
A 32.0-kg body is moving in the direction of the positive x axis with a speed of 234 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 8.0 kg, moves away from the point of explosion with a speed of 445 m/s along the positive y axis. A second fragment, whose mass is 2.5 kg, moves away from the point of explosion with a speed of 443 m/s along the negative x axis.
What is the speed of the third fragment? Ignore effects due to gravity.
How much energy was released in the explosion?
Explanation / Answer
total mass M = 32 kg
velocity of total mass V = 234 i
mass of first piece m1 = 8 kg
velocity of first piece v1 = 445 j m/s
mass of second piece m2 = 2.5 kg
velocity of second piece v2 = -443 i m/s
mass of 3rd piece m3 = M - (m1+m2) = 21.5 kg
velocity of 3rd piece v3 = ?
from momentum conservation momentum before collision =momentum after collision
M*V = m1*v1 + m2*v2 + m3*v3
32*234i = (8*445)j - (2.5*443)i + (21.5*v3)
v3 = 400 i - 165.6 j
speed of 3rd piece v3 = sqrt(400^2+165.6^2) = 433 m/s <<<-----ANSWER
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