Explosion A bomb at rest at the origin of an xy-coordinate system explodes into

Question

Explosion

A bomb at rest at the origin of an xy-coordinate system explodes into three pieces. Just after the explosion, one piece, of mass 3 kg, moves with a velocity of 45 m/s in the negative x-direction, and a second piece, also of mass 3 kg, moves with a velocity of 38 m/s in the negative y-direction. The third piece has a mass of 6 kg.

A bomb at rest at the origin of an xy-coordinate system explodes into three pieces. Just after the explosion, one piece, of mass 3 kg, moves with a velocity of 45 m/s in the negative x-direction, and a second piece, also of mass 3 kg, moves with a velocity of 38 m/s in the negative y-direction. The third piece has a mass of 6 kg. What is the initial momentum of the bomb before the explosion? Submit Answer Tries 0/5 What is the x-component of the velocity of the third piece just after the explosion? Submit Answer Tries 0/S What is the y-component of the velocity of the third piece just after the explosion? Submit Answer Tries 0/5 What is the magnitude of the velocity of the third piece? Submit Answer Tries o/5 Just after the explosion, in what direction is the third piece moving? (Give your answer as an angle measured clockwise from the positive x-axis.)

Explanation / Answer

(a) Initial momentum of the bomb is zero

(b) Let x-component of velocity of third piece be vx

Conserving momentum in x-direction, we get,

[3 * (-45)] + 6vx = 0

=> vx = 22.5 m/s (in the positive x direction)

(c) Conserving momentum in x-direction, we get,

[3 * (-38)] + 6vy = 0

=> vy = 19 m/s (in the positive y-direction)

(d) Magnitude of velocity, v = (vx2 + vy2)1/2 = ((22.5)2 + (19)2)1/2 = 29.45 m/s

(e) Angle that the velocity makes with the positive x-axis in clockwise direction,

= 360o - tan-1(19/22.5) = 319.82o

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