Projectile Motion

A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

A projectile is fired at an angle of $45°$ and reaches the highest point in its path after $2\sqrt{2}$ s. Find the velocity of projectile in $\mathrm{m}/\mathrm{s}$.

The initial velocity of a projectile is $\left(2\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$, where $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are along horizontal and vertical directions, respectively. For $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, the equation of the trajectory will be,

Two seconds after projection, a projectile is moving at $30°$ above the horizontal, after one more second, it is moving horizontally. The initial speed of the projectile is (Take $\left.g=10 {\mathrm{ms}}^{-2}\right)$

Two long parallel plates $A$ and $B$ are separated by a distance of $4 \mathrm{cm}$ with an electric field of $45.5 \mathrm{V} {\mathrm{m}}^{-1}$ between the plates directed normally from plate $A$ to plate $B,$ as shown in the figure. An electron is projected from plate $A$ with velocity $v$ at an angle of $30°$ with the surface of plate $A$. The maximum value of $v$ so that the electron does not hit plate $B$ is
$($Assume gravity free space, charge of electron $=1.6\times {10}^{-19}\mathrm{C}$ and mass of electron $\left.=9.1\times {10}^{-31} \mathrm{kg}\right)$

A body is projected at an angle of $60°$ with the horizontal such that the vertical component of its initial velocity is $40 \mathrm{m} {\mathrm{s}}^{-1}$. The magnitude of velocity of the projectile at one quarter of its time of flight is nearly (Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Two towers $A$ and $B$, each of height $20 \mathrm{m}$ are situated a distance $200 \mathrm{m}$ apart. A body thrown horizontally from the top of the tower A with a velocity $20 {\mathrm{ms}}^{-1}$ towards the tower $B$ hits the ground at point $P$ and another body thrown horizontally from the top of tower $B$ with a velocity $30 {\mathrm{ms}}^{-1}$ towards the tower A hits the ground at point $Q$. If a car starting from rest from $P$ reaches $Q$ in $10$ seconds, the acceleration of the car is _________ $($Acceleration due to gravity $=10 {\mathrm{ms}}^{-2})$

A body is projected horizontally from the top of a tower of height $180 \mathrm{m}$ with a velocity of $20 {\mathrm{ms}}^{-1}$. If acceleration due to gravity is $10 {\mathrm{ms}}^{-2}$ then match the following.

The correct answer is

A stone is thrown with a velocity of $20 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle $60°$ with the horizontal. The speed of the stone when its direction of motion makes $45°$ with the horizontal is

A man of height $7.33 \mathrm{ft}$ releases a stone from the slingshot just above his head. If the stone travels in a vertical direction towards the sky with velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$, then the time it takes to reach the ground is (Assume acceleration due to gravity $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Four projectiles are fired with the same velocities at angles $25°,40°,55°$ and $70°$ with the horizontal. The range of projectile will be largest for the one projected at angle _____.

Two projectiles $A$ and $B$ are projected with the same initial speed. $A$ is launched at an angle $\varphi$ with the horizontal and $B$ at an angle $\varphi$ with the vertical. If $A$ has a range $R_1$ and $B$ has a range $R_2$, then

A projectile is given an initial velocity of $\left(\hat{\mathrm{i}}+\sqrt{3} \hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1},$ where $\hat{\mathrm{i}}$ is along the ground and $\hat{\mathrm{j}}$ is along the vertical. Then, the equation of the path of projectile is $[$Take, $\left.g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$

The velocity of a projectile at the initial point $A$ is $\left(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$. Its velocity (in $\mathrm{m} {\mathrm{s}}^{-1}$) at point $B$ is

An aeroplane is flying in a horizontal direction with a velocity $u$ and at a height of $2000 \mathrm{m}$. When it is vertically below a point $A$ on the ground a food packet is released from it. The packet strikes the ground at point $B$. If $AB=3 \mathrm{km}$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, then the value of $u$ is

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:

The position of a projectile launched from the origin at t = 0 is given by $\overrightarrow{\text{r}}=\left(4\mathrm{0 }\widehat{i}+5\mathrm{0 }\widehat{j}\right)\text{m}$  at t = 2s. If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$  is (take g = 10 ms^-2).

A projectile is given an initial velocity of $\left(\widehat{\mathrm{i}}+2\widehat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$, where $\widehat{\text{i}}$ is along the ground and $\widehat{\text{j}}$ is along the vertically upward direction. If $g=10 m {\mathrm{s}}^{-2}$, the equation of its trajectory is :