Projectile Motion

A ball is projected at an angle of $30°$ above with the horizontal from the top of a tower and strikes the ground in $5 \sec$ at angle of $45°$ with the horizontal. Find the height of the tower and the speed with which it was projected.

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 -----------------------------------

A rifle with a muzzle velocity of $100 \mathrm{m} {\mathrm{s}}^{-1}$ shoots a bullet at a small target $30 \mathrm{m}$ away in the same horizontal line. How high above the target must the gun be aimed so that the bullet will hit the target?

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

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?

An object $A$ is kept fixed at the point  $x=3 m$ and  $y=1.25 m$ on a plank $P$ raised above the ground. At time  $t=0$  the plank starts moving along the  $+x$  direction with an acceleration  $1.5m{s}^{-2}.$  At the same instant a stone is projected from the origin with a velocity $u$ as shown. A stationary person on the ground observes the stone hitting the object during its downward motion at an angle of  $45°$  to the horizontal. All the motions are in the  $x-y$  plane. Find $u$ and the time after which the stone hits the object. Take  $g=10m{s}^{-2}.$          

Two guns situated on the top of a hill of height $10 m$ fire one shot each with the same speed  $5\sqrt{3}m{s}^{-1}$ at some interval of time. One gun fires horizontally and other fires upwards at an angle of  $60°$  with the horizontal. The shots collide in air at point $P$. Find the time interval between the firings.

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 nozzle is situated at a distance of $5.6\mathrm{m}$ above the ground level and is pointed up at angle of $45$ degrees to the horizontal. The diameter of the nozzle is $\frac{1}{\sqrt{\pi }}\mathrm{cm}$ and the jet of water from the nozzle strikes the ground at a horizontal distance of $14\mathrm{m}$. Select the correct statement(s).

A stone is projected with a velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$ at $60°$ to the horizontal. At any instant, the angles of elevation of the stone from the two extremities of the range are $\alpha$ and $\beta$. Then $\tan \alpha +\tan \beta$ equals:

Two bullets are fired horizontally with different velocities from the same height. Which one will reach the ground first?

It is given that a projectile is fired horizontally with a velocity of $98 {\mathrm{ms}}^{-1}$ from the top of a mountain $490 \mathrm{m}$ high. Calculate the velocity of the projectile by which it strikes the ground. $\left(\mathrm{g}=9.8 {\mathrm{ms}}^{-2}\right)$

A projectile has a maximum range of $100 \mathrm{m}$. Neglecting air resistance, what is the maximum height attained by it?

The time of flight of projectile is $10$ second and its range is $500\mathrm{m}.$ The maximum height reached by it is $\left(\mathrm{g}=10{\mathrm{ms}}^{-2}\right)$

A cricket ball is thrown with kinetic energy ${\mathrm{E}}_{\mathrm{k}}$ at an angle $45°$with the horizontal. Its kinetic energy at the highest point will be

From the top of a tower $19.6 \mathrm{m}$ high, a ball is thrown horizontally. If the line joining the point of projection to the point where it hits the ground makes an angle of $45°$ with the horizontal, then the initial velocity of the ball is

A bullet is fired with a velocity $u$ making an angle of $60°$ with the horizontal plane. The horizontal component of the velocity of the bullet when it reaches the maximum height is