Physics Motion in Plane

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1 + β)v, this angle changes to 45°. The value of β is close to:

Starting from the origin at time t = 0, with initial velocity 5ĵ ms⁻¹, a particle moves in the x-y plane with a constant acceleration of (10î + 4ĵ)ms⁻². At time t, its coordinates are (20 m, y₀m). The values of t and y₀ are, respectively:

A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms?²) is of the order of:

A particle is moving along the $x$ $$ -axis with its coordinate with time ' $t$ $$ ' given by $x\left(t\right)=10+8t-3t^2$ ${}^{}$ . Another particle is moving along the $$ $y$ -axis with its coordinate a function of time given by $y\left(t\right)=5-8t^3$ ${}^{}$ . At $t=1\mathrm{s}$ $$ , the speed of the second particle as measured in the frame of the first particle is given as $\sqrt[]{v}$ $\text{exception 25:}$ . Then $v$ $$ (in $$ ) $\mathrm{m}/\mathrm{s}$ is

A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ----------°. (Round off to the Nearest Integer) (Find the angle in degrees)