Physics Motion in Plane

A small block slides down on a smooth inclined plane, starting from rest at time $t=0$ . Let $S_n$ be the distance travelled by the block in the interval $t=n-1$ to $t=n$ . Then, the ratio $\frac{S_n}{S_{n+1}}$  is:

Two transparent media A and B are separated by a plane boundary. The speed of light in those media are $1.5*{10}^8\mathrm{m}/\mathrm{s}$ and $2.0*{10}^8\mathrm{m}/\mathrm{s}$ , respectively. The critical angle for a ray of light for these two media is

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $4{\mathrm{m}\mathrm{s}}^{-1}$ . The ball strikes the water surface after $4\mathrm{s}$ . The height of bridge above water surface is (Take $\mathrm{g}=$ $10{\mathrm{m}\mathrm{s}}^{-2}$  ):

A bullet is fired from a gun at the speed of $280\mathrm{m}/\mathrm{s}$ in the direction ${30}^{\circ }$ above the horizontal. The maximum height attained by the bullet is

$\left(\mathrm{g}=9.8{\mathrm{m}\mathrm{s}}^{-2},\mathrm{s}\mathrm{i}\mathrm{n}?{30}^{?}=0.5\right)$

A person is swimming with a speed of 10m/s at an angle of 120° with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is-----------.

The velocity of a particle is v = v₀ + gt + Ft². Its position is x = 0 at t = 0; then its displacement after time (t = 1) is:

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to [ g is the acceleration due to gravity]:

A balloon is moving up in air vertically above a point A on the ground. When it is at a height h₁, a girl standing at a distance d (point B) from A (see figure) sees it at the angle 45° with respect to the vertical. When the balloon climbs up a future height h₂, it is seen at the angle 60° with respect to the vertical if the girl moves further by a distance 2.464 d (point C). Then the height h₂ is (given tan 30° = 0.5774) :

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: