$A$ plane is revolving around the Earth with a speed of $100\, km/hr$ at a constant height from the surface of the Earth. The change in the velocity as it travels a half circle is ......... $km/hr$.

$A$ particle is performing a uniform circular motion along a circle of radius $R$. In half the period of revolution,its displacement and distance covered are respectively:

Particles $A$ and $B$ are moving with constant velocities along the $x$ and $y$ axes respectively. The graph of the separation $S$ between them with time $t$ is:

At $t = 0$,a projectile is fired from a point $O$ (taken as origin) on the ground with a speed of $50 \, m/s$ at an angle of $53^{\circ}$ with the horizontal. It passes through two points $A$ and $B$,each at a height of $75 \, m$ above the horizontal,as shown in the figure. Find the distance (in meters) of the particle from the origin at $t = 2 \, s$.

Two boys conducted experiments on projectile motion with a stopwatch and noted some readings. As one boy throws a stone into the air at an angle with the horizontal,the other boy observes that after $4 \ s$,the stone is moving at an angle of $30^{\circ}$ to the horizontal,and after another $2 \ s$,it is traveling horizontally. The magnitude of the initial velocity of the stone is (Acceleration due to gravity,$g = 10 \ ms^{-2}$):

The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are $R_{1}, R_{2}$ and $H_{1}, H_{2}$ respectively. Choose the correct option: