Question

An object of mass 2.5 kg has a momentum < 7, 7, 1 > kg m/s At this instant the object is acted on a by a force < 25, 50, 100 > N for 3 x 10-3s What is the momentum of the object at the end of this time interval? < 6.92, 6.85, 0.70 > kg m/s <0.07, 0.15, 0.30> kg m/s < 7.04, 7.08, 1.15 > kg m/s < 7.08, 7.15, 1.30 > kg m/s None of the above

Answer 1

Given Force ,$F_{av}=(25\hat{i}&plus;50\hat{j}&plus;100\hat{k})N$

time,$t=3*10^{-3}s$

initial momentum,$mv_{i}=(7\hat{i}&plus;7\hat{j}&plus;1\hat{k})kgm/s$

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Use Formula $F_{av}*\Delta t=m\Delta v$

$F_{av}*\Delta t=m(v_{f}-v_{i})$

$F_{av}*\Delta t=mv_{f}-mv_{i}$

$F_{av}*\Delta t&plus;mv_{i}=mv_{f}$

$mv_{f}=(25\hat{i}&plus;50\hat{j}&plus;100\hat{k})N*3*10^{-3}s&plus;(7\hat{i}&plus;7\hat{j}&plus;1\hat{k})kgm/s$

$mv_{f}=(25\hat{i}&plus;50\hat{j}&plus;100\hat{k})*3*10^{-3}&plus;(7\hat{i}&plus;7\hat{j}&plus;1\hat{k})$

$mv_{f}=(0.075\hat{i}&plus;0.15\hat{j}&plus;0.3\hat{k})&plus;(7\hat{i}&plus;7\hat{j}&plus;1\hat{k})$

$mv_{f}=(7.075\hat{i}&plus;7.15\hat{j}&plus;1.3\hat{k})$

${\color{Red} mv_{f}=(7.08\hat{i}&plus;7.15\hat{j}&plus;1.30\hat{k})kgm/s}$

ANSWER: Option 4

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