Question

The position of a particle is given by `vecr = 3t hati + 2t^(2) hatj + 5hatk`, where t is in seconds and the coefficients have the proper units for `vecr` to be in metres. The direction of velocity of the particle at `t = 1` s is
A. `53^(@)` with x-axis
B. `37^(@)` with x-axis
C. `30^(@)` with y-axis
D. `60^(@)` with y-axis

Answer 1

Correct Answer - A
Given : `vecr = 3thati +2t^(2)hatj + 5hatk`
Velocity, `vecv = (dvecr)/(dt) = (d)/(dt) (3thati +2t^(2)hatj+5hatk) = 3hati + 4t hatj ms^(-1)`
Let `theta` be angel which the direction of `vecv` makes with the x-axis.Then `tan theta = (v_(y))/(v_(x)) = (4t)/(3) = (4)/(3) or theta = tan^(-1)((4)/(3)) = 53^(@)`