Projectile Motion

A particle is projected in x-y plane with y-axis along vertical, the point of projection being origin. The equation of projectile is $\text{y}=\sqrt{3}\text{x}-\frac{{\text{gx}}^2}{2 }$.  The angle of projectile is ---------------------- and initial velocity is -----------------------------------

From a $10 \mathrm{m}$ high building, a stone $A$ is dropped and simultaneously another identical stone $B$ is thrown horizontally with an initial speed of  $5\mathrm{m} {\mathrm{s}}^{-1}.$ Which one of the following statements is true?

Two towers $AB$ and $CD$ are situated a distance $d$ apart as shown in figure. $AB$ is $20 \mathrm{m}$ high and $CD$ is $30 \mathrm{m}$ high from the ground. An object of mass $m$ is thrown from the top of $AB$ horizontally with a velocity of $10$ $\mathrm{m}{\mathrm{s}}^{-1}$  towards $CD$. Simultaneously another object of mass $2m$ is thrown from the top of $CD$ at an angle of $60°$ to the horizontal towards $AB$ with the same magnitude of initial velocity as that of the first object. The two objects move in the same vertical plane, collide in mid-air and stick to each other. Find the position where the objects hit the ground (from $B$).

A projectile can have the same range $R$ for two angles of projection. If $t_1$ and $t_2$ be the times of flights in the two cases, then the product of the two time of flights is proportional to –

A projectile can have the same range ‘R’ for two angles of projection. If ‘t1’ and ‘t₂’ be the times of flight in the two cases, then the product of the two times of flight is proportional to 

A boy playing on the roof of a 10 m high building throws a ball with a speed of  $10m{s}^{-1 }$ at an angle of  $30°$ with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? [Take g = 10 ms^-2]

A body is projected horizontally from a height of $5 \mathrm{m}$. It reaches the ground at a horizontal distance of $10 \mathrm{m}$. The speed of the particle when it reaches the ground is $\left(g=10 \mathrm{m}{ \mathrm{S}}^{-2}\right)$

The range of a projectile when launched at an angle ${15}^{\mathrm{o}}$ with the horizontal is $1.5 \mathrm{km}$. What will be the range of that projectile when launched with the same velocity at an angle ${45}^{\mathrm{o}}$ to the horizontal?

The maximum range of a gun of horizontal terrain is $16 \mathrm{km}$. If $g=10\mathrm{m}{\mathrm{s}}^{-2},$ then, muzzle velocity of a shell must be

A ball thrown by one player reaches the other in $2 \mathrm{s}$. The maximum height attained by the ball above the point of projection will be $(g=10 {\mathrm{m}\mathrm{s}}^{-2})$

An artillery piece which consistently shoots its shells with the same muzzle speed has a maximum range $R$. To hit a target which is $\frac{R}{2}$ from the gun and on the same level, the elevation angle of the gun should be

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, ${\mathrm{h}}_1$ and ${\mathrm{h}}_2.$ Which of the following is correct?

Two guns $A$ and $B$ can fire bullets at speeds $1\mathrm{ }\mathrm{km} {\mathrm{s}}^{-1}$ and $2 \mathrm{km} {\mathrm{s}}^{-1}$ respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:

A projectile is given an initial velocity of $\left(\widehat{\text{i}}+2\widehat{\text{j}}\right)\text{m}/\text{s}$, where $\widehat{\text{i}}$ is along the ground and $\widehat{\text{j}}$ is along the vertical upward. If $\text{g}=\text{10 m}/{\text{s}}^2$, the equation of its trajectory is :

For angles of projection of projectile at angle (45^o – θ) and (45^o + θ), the horizontal range described by the projectile are in the ratio of

Two stones thrown at different angles have same initial velocity and same range. If $H$ is the maximum height attained by one stone thrown at an angle of 30^o, then the maximum height attained by the other stone is

An arrow is projected into air. Its time of flight is $8 \mathrm{s}$ and range is $200 \mathrm{m}$. The maximum height reached by it is (take $g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$),

A helicopter is flying horizontally at an altitude of $2 \mathrm{km}$ with a speed of $\mathrm{100 }\mathrm{m} {\mathrm{s}}^{-1}$. A packet is dropped from it. The horizontal distance between the point where the packet is dropped and the point where it hits the ground is $(g=\mathrm{10 }\mathrm{m} {\mathrm{s}}^{-2})$,

For a given velocity, a projectile has the same range $R$ for two angles of projection. If $t_1$ and $t_2$ are the time of flight in the two cases, then,