A vessel at rest explodes, breaking into three pieces. Twopieces, having equal m

Question

A vessel at rest explodes, breaking into three pieces. Twopieces, having equal mass, fly off perpendicular to one anotherwith the same speed of 30 m/s. One goes along the negativex-axis and the other along the negative y-axis. The third piece hasthree times the mass of each other piece. What are thedirection and magnitude of its velocity immediately after theexplosion? What is the angle withrespect to the x-axis? What isthe magnitude of its velocity? A vessel at rest explodes, breaking into three pieces. Twopieces, having equal mass, fly off perpendicular to one anotherwith the same speed of 30 m/s. One goes along the negativex-axis and the other along the negative y-axis. The third piece hasthree times the mass of each other piece. What are thedirection and magnitude of its velocity immediately after theexplosion? What is the angle withrespect to the x-axis? What isthe magnitude of its velocity?

Explanation / Answer

Before explosion the vessel is at rest. Therefore the initial momentum of the system both in x and ydirections is zero. Let the masses of the first and second pieces is m. then the mass of the third piece is 3m let the velocity of the third piece is v making anangle with the x-axis. then the x-component of velocity of the third piece will bevcos and the y-component will bevsin Now the momentum of the system in the vertical direction ism(30m/s)-3m(vcos ) and the momentum of the system inthe horizontal direction will be m(30m/s)-3m(vsin )
Now applying the conservation of momentum in both the x and ydirections we should have 0 = m(30m/s)-3m(vcos )   or 3vcos = 30m/s and 0 = m(30m/s)-3m(vsin )   or 3vsin = 30m/s then tan =1 or = 45o with thepositive x-axis
and v = (10m/s)/(cos45o)    = 14.14m/s
Hope this helps you.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.