Topic : motion in a plane

A boy standing on road has to hold umbrella at 30° with vertical to keep the rain away. He throws umbrella and starts running at 10 km/hr he finds that rain drops are hitting his head vertically. The speed of raindrops w.r.t. ground is

Three particles A, B and C are situated at the vertices of an equilateral triangle of side length 3 m. Each of the particles moves with constant speed 2 m/s. A always has its velocity along AB, B along BC and C along CA. After what time will the particles meet each other?

A body of mass 5 kg is acted upon by a force $\vec{F} = (-3\hat{i} + 4\hat{j})$ N. If its initial velocity at $t = 0$ is $\vec{u} = (6\hat{i} - 12\hat{j})$ m/s. The time at which it will just have a velocity along y axis is

A man is swimming with speed 10 km/h in still water crosses a river of width 1 km along the shortest path in 10 minutes. The velocity of river flow is

Position of particle during motion is expressed as $\vec{r} = (5t^2\hat{i} + 3t \hat{j})$ m. The magnitude of acceleration of particle at $t = 0$, is

A train moves northwards with speed 80 km h⁻¹, while a car moves towards east with speed of 60 km h⁻¹. What is magnitude of velocity of train w.r.t. driver of the car?

A particle starts with a velocity of (10 m/s) $\hat{i}$ at $t = 0$ from origin and moves in $x - y$ plane with a constant acceleration of $(2\hat{i} + 3\hat{j})$ m/s$^2$. Speed of the particle at $t = 2$ second will be