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Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

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Calculating the magnetic force on a charged particle

If you're set on using the matrix-determinant method (which isn't any sort of problematic, but isn't the only way to do this), then your matrix should read: $\vec{F}_B=q\left|\matrix{\hat{x}&\hat{y}& …
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What will be final velocity of three charges $q$, $q$, $2q$?

You're only a half-step away. You listed conservation of energy and linear momentum, both of which are due to there being no external forces on the three-charge system. But with no external forces, yo …
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How to solve Kinematics: two objects meeting in the air

You can find the position (as a function of time) for the balloon with simple kinematics: $y_B=200-\dfrac{1}{2}gt_B^2$ (with $g=+9.8\:m/s^2$). After five seconds, the archer shoots the arrow upward …
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