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Question Number 216560 by Tawa11 last updated on 10/Feb/25

An object of mass M, initially at rest at the coordinate origin, explodes into three parts. Fragment A has a mass M/2, and fragments B and C have a mass M/4 each. After the explosion, fragment A moves in the +X direction at 10 m/s and fragment B moves in the +Y direction at 8 m/s. Find the direction and speed of fragment C

An object of mass M, initially at rest at the coordinate origin, explodes into three parts. Fragment A has a mass M/2, and fragments B and C have a mass M/4 each. After the explosion, fragment A moves in the +X direction at 10 m/s and fragment B moves in the +Y direction at 8 m/s. Find the direction and speed of fragment C

Answered by mr W last updated on 12/Feb/25

m_C u_(Cx) +m_A u_(Ax) =0 ⇒u_(Cx) =−((0.5×10)/(0.25))=−20 m/s m_C u_(Cy) +m_B u_(By) =0 ⇒u_(Cy) =−((0.25×8)/(0.25))=−8 m/s ∣u_C ∣=(√((−20)^2 +(−8)^2 ))=21.54 m/s θ=180°+tan^(−1) (8/(20))=201.8°

mCuCx+mAuAx=0⇒uCx=−0.5×100.25=−20m/smCuCy+mBuBy=0⇒uCy=−0.25×80.25=−8m/s∣uC∣=(−20)2+(−8)2=21.54m/sθ=180°+tan−1820=201.8°

Commented by Tawa11 last updated on 11/Feb/25

Thanks sir. I appreciate.

Thankssir.Iappreciate.

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