A17 kg body is moving through space in the positive direction of an x axis with a speed of 320 m/s when, due to an internal explosion, it breaks into three parts. one part, with a mass of 7.9 kg, moves away from the point of explosion with a speed of 190 m/s in the positive y direction. a second part, with a mass of 2.3 kg, moves in the negative x direction with a speed of 420 m/s. what are the (a) x-component and (b) y-component of the velocity of the third part? (c) how much energy is released in the explosion? ignore effects due to the gravitational force.

a) 942.06 m/s

b) - 220.74 m/s

c) 3.7 x 10⁶ J

Explanation:

M = mass of the body = 17 kg

v₀ = initial velocity of body before explosion = 320 i + 0 j + 0 k

m₁ = mass of one part = 7.9 kg

v₁ = velocity of one part after explosion = 0 i + 190 j + 0 k

m₂ = mass of second part = 2.3 kg

v₂ = velocity of second part after explosion = - 420 i + 0 j + 0 k

m₃ = mass of the third part = M - m₁ - m₂ = 17 - 7.9 - 2.3 = 6.8 kg

v₃ = velocity of third part after explosion = ?

Using conservation of momentum

M v₀ = m₁ v₁ + m₂ v₂ + m₃ v₃

17 (320 i + 0 j + 0 k) = (7.9) (0 i + 190 j + 0 k) + (2.3) (- 420 i + 0 j + 0 k ) + (6.8) v₃

5440 i = 1501 j - 966 i + (6.8) v₃

(6.8) v₃ = 6406 i - 1501 j

v₃ = 942.06 i - 220.74 j

x-component = 942.06 m/s

b)

y-component = - 220.74 m/s

c)

Energy released in the explosion is given as

E = (0.5) (M v₀² - m₁ v₁² - m₂ v₂² - m₃ v₃²)

E = (0.5) ((17) (320)² - (7.9) (190)² - (2.3) (420)² + (6.8) (sqrt(942.06² + (- 220.74))²))

E = 3.7 x 10⁶ J

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