Question

The position of an electron is given by `vecr=3.63t hati - 5.73t^2 hatj + 8.16 hatk`, with `t` in seconds and r in meters?

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 `vecv` (give the angle in the range (-180°, 180°])?
-My answers (all incorrect)
a) 9.547
b) -15.07
c)19.61
d)-57.64

Answer 1

On the basis of given text

Explanation:

Position of an electron is given by `vecr=3.63thati−5.73t^2hatj+8.16hatk`

Velocity `vecv` is first differential of position vector with time.

`vecv=d/dt(3.63thati−5.73t^2hatj+8.16hatk)`
`=>vecv=3.63hati−11.46thatj`

(a) `3.63\ ms^-1`
(b) `-11.46t\ ms^-1` For `t=2.63\ s`, we get

`-11.46xx2.63=-30.140\ ms^-1`

(c) `|vecv|=sqrt((3.63)^2+(-30.140)^2)`

`|vecv|=30.578\ ms^-1`

(d) If `θ` is the angle made by velocity with `x`-axis at time `t`

`tantheta=v_y/v_x`

Inserting calculated values

`tan\ θ=(-30.140)/3.63`, (`4th` quadrant)
`theta=-83.1^@`, relative to the positive direction of the `x`-axis, in the desired range.

(Clockwise being positive direction and anti-clockwise being negative direction)