Motion in Two Dimensions - Motion in a Plane

The speed of swimmer in still water is 10 m/s. The speed of river water is 5 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by: ____________.

A projectile is projected with a velocity of `(3hati + 4hatj)` m/s. The horizontal range of the projectile will be ______.

A projectile thrown from the ground has an initial speed u and its direction makes an angle θ with the horizontal. If at maximum height from the ground, the speed of the projectile is half its initial speed of projection, then the maximum height reached by the projectile is ______.

`["g = acceleration due to gravity", sin30^circ = cos60^circ = 0.5, cos30^circ = sin60^circ = sqrt3"/"2]`

The velocity of a projectile at the initial point A is `(2 hat "i" + 3 hat "j")` m/s. Its velocity (in m/s) at point B is ______.

Two bodies A and B move in the same straight line starting from the same position. Body A moves with constant velocity u and B moves with constant acceleration a. When their velocities become equal, the distance between them is ______.

Two bodies of masses m₁ and m₂ are connected a light string which passes over a frictionless massless pulley. If the pulley is moving upward with uniform acceleration `"g"/2`, then tension in the string will be ______.