Two projectiles are launched from the same point with the same speed $u$. One is launched at an angle $heta$ and the other at $(90^\circ - heta)$ with the horizontal. What is the minimum distance between these two projectiles during their flight?

The potential energy of a projectile at its maximum height is equal to its kinetic energy there. If the velocity of projection is $20\,m{s^{ - 1}}$ its time of flight is $\left( {g = 10\,\,m{s^{ - 2}}} \right)$

A particle is projected at an angle of ${60^0}$ above the horizontal with a speed of $10{\rm{\;m}}{{\rm{s}}^{ - 1}}$. After some time the direction of its velocity makes an angle of ${30^0}$ above the horizontal. The speed of the particle at this instant is

The retardation experienced by a moving motor boat, after its engine is cut off, is given by

$\frac{{du}}{{dt}} = - k{v^3},$, where k is a constant.

If ${v_0}$ is the magnitude of the velocity at cut-off, the magnitude of the velocity at time t after the cut-off is

A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of 1 km. The minimum time taken around a round trip is

A ball is projected with kinetic energy E. at an angle of ${45^0}$ to the horizontal. At the highest point during its flight, its kinetic energy will be

Neglecting the air resistance, the time of flight of a projectile is determined by

A stone is projected from the ground with velocity $50{\rm{\;m}}{{\rm{s}}^{ - 1}}$ and angle of ${30^0}$. It crosses a wall after 3 s. How far beyond the wall the stone will strike the ground?

Two projectiles are launched from the same point with the same speed $v_0$ at angles $heta$ and $(90^\circ - heta)$ with the horizontal. Let $R_1$ and $R_2$ be their horizontal ranges, and $T_1$ and $T_2$ be their times of flight. Which of the following is correct?

A small toy car is launched with a fixed initial speed up a smooth incline. The car travels a distance $d$ along the incline when the angle of inclination is $heta$. If the angle is changed, which of the following angles will result in the car travelling the same distance $d$ along the incline?

A small block is projected up a frictionless inclined plane with an initial speed 'u'. The plane is inclined at an angle 'α' with the horizontal. The block travels a distance 'd' along the plane before coming to rest. If the angle of inclination is doubled to '2α', while keeping the initial speed 'u' constant, will the distance traveled by the block along the plane increase, decrease, or stay the same? Assume the launch angle with respect to the horizontal remains constant.