A toy car of mass $100 \mathrm{~g}$ is moving with velocity of $(\hat{i}+2 \hat{j}-3 \hat{k}) m$, then the…

A toy car of mass $100 \mathrm{~g}$ is moving with velocity of $(\hat{i}+2 \hat{j}-3 \hat{k}) m$, then the kinetic energy of the car is
  1. $7 \mathrm{~J}$
  2. $70 \mathrm{~J}$
  3. $0.7 \mathrm{~J}$
  4. $0.07 \mathrm{~J}$

Solution

Mars, $m=100 \mathrm{~g}=0.1 \mathrm{~kg}$ velocity, $\vec{v}=\hat{i}+2 \hat{j}-3 \hat{k}$ Magnitude of velocity, $|v|=\sqrt{(\hat{i})^2+(2 \hat{j})^2+(-3 \hat{k})^2}=\sqrt{14}$ Kinetic energy is given as, $\mathrm{K}=\frac{1}{2} \mathrm{mv}^2=\frac{1}{2} \times 0.1 \times(\sqrt{14})^2=0.7 \mathrm{~J}$

Asked in: AP EAMCET 2023 (18 May Shift 1)

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