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 the X-Y plane. $2 \mathrm{s}$ after projection, the velocity of the particle makes an angle $45°$ with the X-axis. $4 \mathrm{s}$ after projection, it moves horizontally. Find the velocity of projection (use $\mathrm{g} = 10 \mathrm{m} {\mathrm{s}}^{-2}$)

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?

A ball whose kinetic energy is $E$, is thrown at an angle of $45°$  with the horizontal. Its kinetic energy at the highest point of its flight will be:

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  $g=10m{s}^{-2}.$          

A large heavy box is sliding without friction down a smooth plane of inclination  $\theta$ . From a point $P$ on the bottom of the box, a particle is projected inside the box. The initial speed of the particle with respect to the box is $u$ and the direction of projection makes an angle $\alpha$ with the bottom as shown in the figure:

If the horizontal displacement of the particle as seen by an observer on the ground is zero, find the speed of the box with respect to the ground at the instant when the particle was projected.

A large heavy box is sliding without friction down a smooth plane of inclination $\text{θ}$. From a point $\mathrm{P}$ on the bottom of the box, a particle is projected inside the box. The initial speed of the particle with respect to the box is $u$ and the direction of projection makes an angle $\alpha$ with the bottom as shown in the figure:



Find the distance along the bottom of the box between the point of projection $\mathrm{P}$ and the point $\mathrm{Q}$ where the particle lands. [Assume that the particle does not hit any other surface of the box. Neglect air resistance]

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 body is projected at an angle of $60°$ with me horizontal with a speed of $10\sqrt{3} {\mathrm{ms}}^{-1}$. What is the angle with horizontal after $1.5 \sec$ ? $\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$

Two Particles $A$ and $B$ are projected simultaneously from the two towers of height $10 \mathrm{m}$ and $20 \mathrm{m}$. Particle $A$is projected with an initial speed of $10\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$ at an angle of $45°$with the horizontal while particle$B$is projected horizontally with speed $10 \mathrm{m} {\mathrm{s}}^{-1}$. If they collide in air, what is the distance $d$ between the towers (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R.$

Assertion A: When a body is projected at an angle $45°,$ its range is maximum.

Reason R: For maximum range, the value of sin $2\theta$ should be equal to one.

In the light of the above statements, choose the correct answer from the options given below:

The trajectory of projectile, projected from the ground is given by $y=x-\frac{x^2}{20}$. Where $x$ and $y$ are measured in meter. The maximum height attained by the projectile will be.

Two projectiles are projected at $30°$ and $60°$with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

Which of the following quantities remain constant during projectile motion?

A cart moves with a constant speed along a horizontal circular path. From the cart a body is thrown vertically up, with respect to the cart. The body will:

(a) land outside the circular path

(b) land somewhere on the path.

(c) follow a parabolic path

(d) follow an elliptical path

Which of the above statements are correct?

An object is projected in the air with initial velocity $u$at an angle $\theta$. The projectile motion is such that the horizontal range $R$ , is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be

The angle of projection is $45°$. The height$h$is