Please show all work and round to 4 decimal places if possible. Thanks! A 25.0-k

Question

Please show all work and round to 4 decimal places if possible. Thanks!

A 25.0-kg body is moving in the direction of the positive x axis with a speed of 221 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 352 m/s along the positive y axis. A second fragment, whose mass is 3.5 kg, moves away from the point of explosion with a speed of 496 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

let M = 25 kg, V = 221 m/s

m1 = 8 kg, v1 = 352 m/s

m2 = 3.5 kg, v2 = 496 m/s

m3 = M - (m1+m2)

= 25 - (8 + 3.5)

= 13.5 kg

v3 = ?

let v3x and v3y are the components of v3.

Apply conservation of momentum in x-direction

M*vx = m1*v1x + m2*v2x + m3*v3x

25*221 = 8*351 + 0 + 13.5*v3x

==> v3x = (25*221 - 8*351)/13.5

= 201 m/s

Apply conservation of momentum in x-direction

M*vy = m1*v1y + m2*v2y + m3*v3y

0 = 0 + 3.5*496 + 13.5*v3y

==> v3y = -3.5*496/13.5

= -128.6 m/s

v3 = sqrt(v3x^2 + v3y^2)

= sqrt(201^2 + 128.6^2)

= 239 m/s <<<<<<<<---------------Answer

ENergy released in the explosion = change in kinetic energy

= 0.5*m1*v1^2 + 0.5*m2*v2^2 + 0.5*m3*v3^2 - 0.5*M*V^2

= 0.5*8*352^2 + 0.5*3.5*496^2 + 0.5*13.5*239^2 - 0.5*25*221^2

= 7.01*10^5 J <<<<<<<<---------------Answer

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