A 37.0- kg body is moving in the direction of the positive x axis with a speed o

Question

A 37.0-kg body is moving in the direction of the positive x axis with a speed of 243 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 10.0 kg, moves away from the point of explosion with a speed of 397 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 337 m/s along the negative x axis.

a.) What is the speed of the third fragment? Ignore effects due to gravity.

b.) How much energy was released in the explosion?

Explanation / Answer

here,

initial mass , M = 37 kg

initial speed , u = 243 m/s i

for m1 = 10 kg , speed of 1 , v1 = 397 j m/s

for m2 = 3.5 kg is at speed , v2 = - 337 i m/s

a)

m3 = M - m1 - m2 = 23.5 kg

let the final speed of 3 be v3

using conservation lof momentum

M * u = m1 * v1 + m2 * v2 + m3 * v3

37 * 243 i = 10 * 397 j - 3.5 * 337 i + 23.5 * v3

v3 = 432.8 i - 169 j m/d

the speed , |v3| = sqrt(432.8^2 + 169^2) = 446.6 m/s

b)

the energy released in the explosion,E = 0.5 * M * u^2 - 0.5 * m1 * v1^2 - 0.5 * m2 * v2^2 - 0.5 * m3 * v3^2

E = 0.5 * 37 * 243^2 - 0.5 * 10 * 397^2 - 0.5 * 3.5 * 337^2 - 0.5 * 23.5 * 446.6^2 J

E = - 2.2 * 10^6 J

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