The position of an electron is given by r Overscript right-arrow EndScripts equa

Question

The position of an electron is given by r Overscript right-arrow EndScripts equals 3.50 t i Overscript EndScripts minus 1.27 t Superscript 2 Baseline j Overscript EndScripts plus 1.49 k Overscript EndScripts, with t in seconds and r Overscript right-arrow EndScripts in meters. At t = 2.90 s, what are (a) the x-component, (b) the y-component, (c) the magnitude, and (d) the angle relative to the positive direction of the x axis, of the electron's velocity v Overscript right-arrow EndScripts(give the angle in the range (-180°, 180°])? The position of an electron is given by r Overscript right-arrow EndScripts equals 3.50 t i Overscript EndScripts minus 1.27 t Superscript 2 Baseline j Overscript EndScripts plus 1.49 k Overscript EndScripts, with t in seconds and r Overscript right-arrow EndScripts in meters. At t = 2.90 s, what are (a) the x-component, (b) the y-component, (c) the magnitude, and (d) the angle relative to the positive direction of the x axis, of the electron's velocity v Overscript right-arrow EndScripts(give the angle in the range (-180°, 180°])?

Explanation / Answer

Given eqn of position is:

r = 3.5 t i - 1.27 t^2 j + 1.49 k

We know that speed is:

v = dr/dr = d(3.5 t i - 1.27 t^2 j + 1.49 k)/dt

v = 3.5 i - 2.54 t j + 0 k

for t = 2.9 s

a)we have,

v = 3.5 i - 2.54 t j + 0 k

v(x) = 3.5 m/s

b)we have,

v = 3.5 i - 2.54 t j + 0 k

vy = -2.54 x 2.9 = -7.366 j

Hence, v(y) = -7.366 m/s

c)theta = tan^-1(vy/vx)

theta = tan^-1(-7.366/3.5) = -64.58 deg

Hence, theta = -64.58 deg

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