Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles $\theta _1$ and $\theta_2$ respectively from the horizontal, then answer the following question

The trajectory of particle $1$ with respect to particle $2$ will be

A particle has an initial velocity of ($3\hat i + 4\hat j)\;ms^{-1}$ and an acceleration of $(0.4\hat i + 0.3\hat j)\;ms^{-1}$ Its speed after $10\;s$ is:

Which is the direction of instantaneous velocity for angular path ?

A hiker stands on the edge of a cliff $490\; m$ above the ground and throws a stone horizontally with an initial speed of $15 \;m/ s$. Neglecting air resistance, find the time taken by the stone to reach the ground, and the speed with which it hits the ground. (Take $g = 9.8 \;m /s^2$ ).

Find the speed of the intersection point $O$ of the two wires if the wires starts moving perpendicular to itself with speed $v$ as shown in figure.

A particle has initial velocity $(2\hat i + 3\hat j ) $ and has acceleration $(0.3\,\hat i + 0.2\,\hat j)$ . Its speed after $10\,s$ is