Horizontal Projectile from Elevation

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.

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.

If an object is thrown horizontally with an initial speed $10 {\mathrm{ms}}^{-1}$ from the top of a building of height $100 \mathrm{m}$. What is the horizontal distance covered by the particle?

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 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 $(g=\mathrm{10 }\mathrm{m} {\mathrm{s}}^{-2})$,

A ball is projected horizontally. The range is $3H$ and height of projection is $H.$ Find the speed of projection and actual velocity at the bottom respectively. (Assume g is the acceleration due to gravity)

A train is travelling on a straight horizontal track with a constant acceleration of 2 m/s² across a bridge over a river. When the velocity of the train is 25 m/s, a man inside one of the cars throws a stone horizontally out of a window in a direction perpendicular to direction of motion of the train with a speed of 5 m/s relative to himself. In the absence of air resistance the stone hits the water at point P, 40 m in a horizontal direction from track. Consider point of projection as origin and cartesian coordinate system as shown in diagram.  (Take g = 10 m/s²)

 Based on above information answer the following questions.

At the instant when stone hits the water, the coordinate of car window from which stone is projected, is

For next two question please follow the same

A train is travelling on a straight horizontal track with a constant acceleration of 2 m/s² across a bridge over a river. When the velocity of the train is 25 m/s, a man inside one of the cars throws a stone horizontally out of a window in a direction perpendicular to direction of motion of the train with a speed of 5 m/s relative to himself. In the absence of air resistance the stone hits the water at point P, 40 m in a horizontal direction from track. Consider point of projection as origin and cartesian coordinate system as shown in diagram.  (Take g = 10 m/s²)

Based on above information answer the following questions.
The coordinate of point P is

A hiker stands on the edge of a cliff $490\mathrm{ }\mathrm{m}$ above the ground and throws a stone horizontally with a speed of $15\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$. The time taken by the stone to reach the ground is _____ $\mathrm{s}$.

What is the ratio of velocities of two particles thrown from a height $h$ and velocity $u$, one vertically downwards and another horizontally when they reach the earth’s surface?

A staircase contains three steps each $10 \mathrm{cm}$ high and $20 \mathrm{cm}$ wide. What should be the minimum horizontal velocity of the ball rolling off the uppermost plane so as to hit directly the lowest plane? (in ${\mathrm{ms}}^{-1}$)

A $100\mathrm{ }\mathrm{kg}$ gun fires a ball of $1\mathrm{ }\mathrm{kg}$ horizontally from a cliff of height $500 \mathrm{m}$. It falls on the ground at a distance of $400 \mathrm{m}$ from the bottom of the cliff. The recoil velocity of the gun is $(\text{Take}\mathrm{ }g=10\mathrm{ }{\mathrm{ms}}^{-2})$

An aeroplane flying horizontally with a speed of $360\mathrm{ }\mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}$ releases a bomb at a height of $490\mathrm{ }\mathrm{m}$ from the ground. If $g=9.8\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$, it will strike the ground at

A particle $A$ is projected from the ground with an initial velocity of $10\mathrm{ }\mathrm{m}{\mathrm{s}}^{-1}$ at an angle $60°$ with horizontal. From what height should another particle $B$ be projected horizontally with velocity $5\mathrm{ }\mathrm{m}{\mathrm{s}}^{-1}$ so that both the particles collide in ground at point $C$ if both are projected simultaneously ($\mathrm{g}=10\mathrm{m}{\mathrm{s}}^{-\mathrm{2)}}$

A ball is thrown upwards with a speed $u$ from a height $h$ above the ground. The time taken by the ball to hit the ground from maximum height is,

A ball falls from a table top with initial horizontal speed $V_0$ . In the absence of air resistance, which of the following statement is correct

From the top of a tower, two balls are thrown horizontally with velocities $u_1 \text{and} u_2$ in opposite directions. If their velocities are perpendicular to each other just before they strike the ground, the height of the tower is

A ball is thrown horizontally from a point $O$ with speed $20 \mathrm{m} {\mathrm{s}}^{-1}.$ Ball strikes incline plane along normal to it after two seconds find value of angle of inclination of inclined plane.

Two balls are thrown horizontally from the top of a tower with velocities $v_1$ and $v_2$ in opposite directions at the same time. After how much time, the angle between velocities of balls becomes ${90}^o$ ?

A bomb is dropped on an enemy post by an aeroplane flying horizontally with a velocity of $60\mathrm{ }\mathrm{km}\mathrm{ }{\mathrm{h}}^{-1}$ and at a height of $490 \mathrm{m}$. At the time of dropping the bomb, how far the aeroplane should be from the enemy post so that the bomb may directly hit the target?