Particles moving along the axes.

[niyati]

Particle 1 is moving on the x-axis with an acceleration of 5.45 m/s^2 in the positive x-direction. Particle 2 is moving on the y-axis with an acceleration of 7.56 m/s^2 in the negative y-direction. Both particles were at rest at the origin at t = 0 s. Find the speed of particle 1 with respect to particle 2 at 6.15 s. Answer in units of m/s.

I'm not sure what the question is asking for. The whole "with respect to" slightly confuses me. In the x-direction, the velocity after 6.15 is 33.5175. In the negative y-direction, it is 46.494. ...am I just suppose to draw the hypotenuse to the triangle formed and find that length?

 

[Avodyne]

Yes. The velocity of #1 with respect to #2 is $$\vec{v}_1-\vec{v}_2$$. Since $$\vec{v}_1$$ is perpendicular to $$\vec{v}_2$$, the speed (which is the magnitude of $$\vec{v}_1-\vec{v}_2$$) is $$(v_1^2+v_2^2)^{\scriptstyle{1/2}}$$.

 

[niyati]

Thank you!