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A radio-controlled model airplane has a momentum given by $\left[\left(-0.75 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}^{3}\right) t^{2}+\right.$ $(3.0 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}) ] \hat{\mathrm{i}}+\left(0.25 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}^{2}\right) \hat{t}$ What are the $x-y$ , and z-components of the net force on the airplane?

$F_{x}=-1.5 t \mathrm{N} / \mathrm{s} \quad F_{y}=0.25 \mathrm{N} \quad-\quad F_{z}=0$

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University of Michigan - Ann Arbor

Numerade Educator

University of Washington

University of Winnipeg

in this question, the radio controlled airplane is moving with a momentum given by this expression. Then we have to calculate what is the Net force that is acting on the airplane. For that, we have to use Newton's second law in this form. So Newton's second law tells us that the net force that is acting on something is equals to the derivative off the momentum with respect to time. This is another way off state in the F equals to the mass times acceleration. Second law To show this question, all you have to do in practice is take the time derivative off this quantity. So let us do that. The time derivative off the momentum we've respect forced The time is equals to the derivative off this term with respect to time. So we have minus 0.75 is just a constant. So the derivative do not act on constant. Now we have the time derivative off this weird. This is two times T plus three the derivative off a constant +30 So the tree vanishes from the derivative and then we multiply that quantity By that vector, I, which is a constant vector pointing in the X direction. Now we go to the next term. In the next term, we have 0.25 times t The derivative off tea with respect to T is equal to one. Then we have 0.25 times one times the unit Vector J, which is a unit vector pointing in the Y direction now organizing that in a better way. We have the following dp DT is equals to minus 1.5 times t times I plus 0.25 times J. Then you just have to identify disease. The X component off the net force. This is the white component off the net force. And for those that component, we have zero because there is no that component off the force. So this is the answer to this question.

Brazilian Center for Research in Physics