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
Answered by mr W last updated on 12/Feb/25
$${m}_{{C}} {u}_{{Cx}} +{m}_{{A}} {u}_{{Ax}} =\mathrm{0} \\ $$$$\Rightarrow{u}_{{Cx}} =−\frac{\mathrm{0}.\mathrm{5}×\mathrm{10}}{\mathrm{0}.\mathrm{25}}=−\mathrm{20}\:{m}/{s} \\ $$$${m}_{{C}} {u}_{{Cy}} +{m}_{{B}} {u}_{{By}} =\mathrm{0} \\ $$$$\Rightarrow{u}_{{Cy}} =−\frac{\mathrm{0}.\mathrm{25}×\mathrm{8}}{\mathrm{0}.\mathrm{25}}=−\mathrm{8}\:{m}/{s} \\ $$$$\mid{u}_{{C}} \mid=\sqrt{\left(−\mathrm{20}\right)^{\mathrm{2}} +\left(−\mathrm{8}\right)^{\mathrm{2}} }=\mathrm{21}.\mathrm{54}\:{m}/{s} \\ $$$$\theta=\mathrm{180}°+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{8}}{\mathrm{20}}=\mathrm{201}.\mathrm{8}° \\ $$
Commented by Tawa11 last updated on 11/Feb/25
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{appreciate}. \\ $$