A mosquito is moving with a velocity $\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }\, m / s$ and accelerating in uniform conditions. What will be the direction of mosquito after $2 \,s$ ?

  • [JEE MAIN 2021]
  • A

    $\tan ^{-1}\left(\frac{2}{3}\right)$ from $x-$ axis

  • B

    $\tan ^{-1}\left(\frac{2}{3}\right)$ from $y$ -axis

  • C

    $\tan ^{-1}\left(\frac{5}{2}\right)$ from $y$ -axis

  • D

    $\tan ^{-1}\left(\frac{5}{2}\right)$ from $x$ -axis

Similar Questions

A football is kicked into the air vertically upwards. What is its

$(a)$ acceleration and

$(b)$ velocity at the highest point ?

The coordinates of a particle moving in a plane are given by $x = a\cos (pt)$ and $y(t) = b\sin (pt)$ where $a,\,\,b\,( < a)$ and $p$ are positive constants of appropriate dimensions. Then

  • [IIT 1999]

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $v$ and other with a uniform acceleration $a.$ If $\alpha$ is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by

The initial position of an object at rest is given by $3 \hat{i}-8 \hat{j}$ It moves with constant acceleration and reaches to the position $2 \hat{i}+4 \hat{j}$ after $4 \,s$. What is its acceleration?

A boy is moving with a constant speed $v$ on a small trolley towards a distant circle as shown in the figure. A point mass is moving on the circle with a constant speed $v$, what is the frequency of change in magnitude of relative velocity of the point mass, as observed by the boy.