Question

a car is moving along a line y=x at 10m/s . find component of velocity vector on the vector i+j+k
please answer
thnks

Answer 1

See figure to the left.

$$\varphi = \operatorname {arctg} \left(\frac {1}{\sqrt {2}}\right) \approx 35.26$$ $$\begin{array}{l} v _ {\bar {i} + \bar {j} + \bar {k}} = v * \cos (\varphi) = v * \frac {1}{\sqrt {1 + t g ^ {2} \varphi}} = v * \sqrt {\frac {2}{3}} \\ = 10 \left[ \mathrm{m/s} \right] * 0.82 = 8.2 \left[ \mathrm{m/s} \right] \\ \end{array}$$

Answer: $v_{\bar{i} + \bar{j} + \bar{k}} = 8.2 \left[ \frac{\mathrm{m}}{\mathrm{s}} \right]$.