Projectile from a Height

Q. A marble with speed 20 cm/s rolls off the edge of a table 80 cm high. How far horizontally from the table edge does the marble strike the floor? (answer in $\text{cm}$ and take $g=10m/s^2$)

Q. Two bodies are projected horizontally at the same time from the top of a tower of height $78.4\text{m}$. If their velocities are $30\text{m/s}$ and $40\text{m/s}$ respectively, find the difference between the times taken by them for hitting the ground.

1. $2\text{sec}$
2. $4\text{sec}$
3. $1\text{sec}$
4. zero

Q. A body of mass $m$ is projected horizontally with a velocity $v$ from the top of a tower of height $h$ and it reaches the ground at a distance $x$ from the foot of the tower. If a second body of mass $2m$ is projected horizontally from the top of a tower of height $2h$, it reaches the ground at a distance $2x$ from the foot of the tower. The horizontal velocity of the second body is

1. $v$
2. $2v$
3. $\sqrt{2}v$
4. $\frac{v}{2}$

Q. A helicopter is flying horizontally at an altitude of $2\text{km}$ with a speed of $100{\text{ms}}^{-1}$. 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 $(g=10{\text{ms}}^{-2})$

1. $2\text{km}$
2. $0.2\text{km}$
3. $20\text{km}$
4. $4\text{km}$

Q. A body is projected horizontally from the top of a tower with an initial velocity of $18{\text{ms}}^{-1}$. It hits the ground at an angle of ${45}^{\circ }$ with horizontal. What is the vertical component of velocity when the body strikes the ground?

1. $9\text{m/s}$
2. $9\sqrt{2}\text{m/s}$
3. $18\text{m/s}$
4. $18\sqrt{2}\text{m/s}$

Q. A plane is flying horizontally at $98m/s$ and releases an object which reaches the ground in 10 seconds. The angle made by it when it hits the ground is

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${75}^{\circ }$

Q. Ball bearings leave the horizontal trough with a velocity of magnitude $u$ and fall through the $70mm$ diameter hole as shown. Calculate the permissible range of $u$ which will enable the balls to enter the hole. Take the dotted positions to represent the limiting conditions. (Take $g=10m/s^2\text{and}\sqrt{10}=3.2$)

1. $u=0.62m/s$ to $1.01m/s$
2. $u=0.76m/s$ to $1.16m/s$
3. $u=0.43m/s$ to $1.91m/s$
4. $u=0.80m/s$ to $1.03m/s$

Q. Ball bearings leave the horizontal trough with a velocity of magnitude $u$ and fall through the $70mm$ diameter hole as shown. Calculate the permissible range of $u$ which will enable the balls to enter the hole. Take the dotted positions to represent the limiting conditions. (Take $g=10m/s^2\text{and}\sqrt{10}=3.2$)

1. $u=0.62m/s$ to $1.01m/s$
2. $u=0.76m/s$ to $1.16m/s$
3. $u=0.43m/s$ to $1.91m/s$
4. $u=0.80m/s$ to $1.03m/s$

Q. A motorcycle stunt rider rides off the edge of a cliff. Just at the edge, his velocity is horizontal with magnitude $9.0\text{m/s}$. Find the motorcycle’s distance from the edge of the cliff and velocity after $0.5\text{s}$.

1. Distance $=\frac{349}{4}\text{m}$, Velocity $=\sqrt{106}\text{m/s}$
2. Distance $=\frac{\sqrt{349}}{2}\text{m}$, Velocity $=\sqrt{106}\text{m/s}$
3. Distance $=\frac{\sqrt{349}}{4}\text{m}$, Velocity $=106\text{m/s}$
4. Distance $=\frac{\sqrt{349}}{4}\text{m}$, Velocity $=\sqrt{106}\text{m/s}$

Q. A bullet with muzzle velocity $500\text{m/s}$ is to be shot at a target $1000\text{m}$ away in the same horizontal line. At what height above the target, a rifle must be aimed so that the bullet will hit the target ?

1. $30\text{m}$
2. $20\text{m}$
3. $65\text{m}$
4. $40\text{m}$

Q. A marble is to be thrown horizontally from a height of $19.6\text{cm}$ above the ground so that it hits another marble on the ground $2\text{m}$ away. The velocity with which the marble should be thrown is

1. $5{\text{ms}}^{-1}$
2. $10{\text{ms}}^{-1}$
3. $5{\text{ms}}^{-1}$
4. $20{\text{ms}}^{-1}$

Q. As shown in the figure a projectile is fired with a horizontal velocity of $330\text{m/s}$ from the top of a cliff $80\text{m}$ high. How far from the foot of the cliff will it strike?

1. $660\text{m}$
2. $1320\text{m}$
3. $330\text{m}$
4. $2640\text{m}$

Q. A bomb is dropped on an enemy post by an aeroplane flying horizontally with a velocity of $60{\text{kmh}}^{-1}$ and at a height of $490\text{m}$. 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?

1. $\frac{400}{3}\text{m}$
2. $\frac{500}{3}\text{m}$
3. $\frac{1700}{3}\text{m}$
4. $498\text{m}$

Q. A body is projected horizontally with a velocity of $10\text{m/s}$ from the top of an inclined plane of angle ${45}^{\circ }.$ If the body hit the foot of the plane, the height of the plane (in $\text{m}$) is

1. $10\text{m}$
2. $20\text{m}$
3. $30\text{m}$
4. $40\text{m}$

Q.

An aeroplane flying 490 m above ground level at 100 m/s, releases a block. How far on ground will it strike

1. 0.1 km

2. 1 km

3. 2 km

4. None

Q. An object is thrown between two tall buildings $180\text{m}$ from each other. The object is thrown horizontally from a window $55\text{m}$ above ground from one building to a window $10.9\text{m}$ above ground in the other building. Find out the speed of projection in $\text{m/s}$. (Use $g=9.8{\text{m/s}}^2$)

Q. A projectile is fired horizontally with a speed of $98{\text{ms}}^{-1}$ from the top of a hill $490\text{m}$ high. Find
(i) The time taken to reach the ground
(ii)The distance of the target from the hill and
(iii)The velocity with which the projectile hits the ground. (take $g=9.8{\text{m/s}}^2$)

1. (i) $5\text{s}$, (ii) $490\text{m}$, (iii) $110\text{m/s}$
2. (i) $10\text{s}$, (ii) $980\text{m}$, (iii) $98\sqrt{2}\text{m/s}$
3. (i) $15\text{s}$, (ii) $1470\text{m}$, (iii) $110\text{m/s}$
4. (i) $5\text{s}$, (ii) $980\text{m}$, (iii) $98\text{m/s}$

Q. Two bodies are projected from the top of a tower in opposite directions with velocities of $u_1$ and $u_2$ simultaneously. Find the time when their velocities are mutually perpendicular.

1. $\frac{2\sqrt{u_1{u}_2}}{g}$
2. $\frac{\sqrt{u_1{u}_2}}{g}$
3. $\frac{\sqrt{4u_1{u}_2}}{g}$
4. $\frac{\sqrt{8u_1{u}_2}}{g}$

Q. A projectile is fired horizontally with a speed of $98{\text{ms}}^{-1}$ from the top of a hill $490\text{m}$ high. Find
(i) The time taken to reach the ground
(ii)The distance of the target from the hill and
(iii)The velocity with which the projectile hits the ground. (take $g=9.8{\text{m/s}}^2$)

1. (i) $5\text{s}$, (ii) $490\text{m}$, (iii) $110\text{m/s}$
2. (i) $10\text{s}$, (ii) $980\text{m}$, (iii) $98\sqrt{2}\text{m/s}$
3. (i) $15\text{s}$, (ii) $1470\text{m}$, (iii) $110\text{m/s}$
4. (i) $5\text{s}$, (ii) $980\text{m}$, (iii) $98\text{m/s}$

Q. A ball is projected horizontally from top of a 80 m deep well with velocity $10m/s.$ Then particle will fall on the bottom at a distance of (all the collisions with the wall are elastic and wall is smooth)
(Take $g=10m/s^2$)

1. $5m$ from A
2. $4m$ from B
3. $2m$ from A
4. $2m$ from B

Q. As shown in the figure, a projectile is fired with a horizontal velocity of $330\text{m/s}$ from the top of a cliff $80\text{m}$ high. (a) How long will it take for the projectile to strike the level ground at the base of the cliff? (b) How far from the foot of the cliff will it strike? (c) With what velocity will it strike?
(Take $g=10m/s^2$)

1. (a) $16\text{s}$ (b) $5280\text{m}$ (c) $366.7\text{m/s}$
2. (a) $4\text{s}$ (b) $1320\text{m}$ (c) $330\text{m/s}$
3. (a) $4\text{s}$ (b) $1320\text{m}$ (c) $332.4\text{m/s}$
4. (a) $8\text{s}$ (b) $2640\text{m}$ (c) $332.4\text{m/s}$

Q. A bomb is dropped on an enemy post by an aeroplane flying horizontally with a velocity of $60{\text{kmh}}^{-1}$ and at a height of $490\text{m}$. 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?

1. $\frac{400}{3}\text{m}$
2. $\frac{500}{3}\text{m}$
3. $\frac{1700}{3}\text{m}$
4. $498\text{m}$

Q. A body is projected from the top of a tower of height $32\text{m}$ with a velocity of $20\text{m/s}$ at an angle of ${37}^{\circ }$ above the horizontal. The time of flight of the projectile is
(Take $g=10m/s^2$)

1. $\frac{8}{5}\text{s}$
2. $2\text{s}$
3. $8\text{s}$
4. $4\text{s}$

Q. A body is thrown with a velocity of $20{\text{ms}}^{-1}$ from a building of height $15\text{m}$. If the angle of projection is ${30}^{\circ }$above the horizontal find the time of flight
(Take $g=10m/s^2$)

1. $1\text{s}$
2. $3\text{s}$
3. $5\text{s}$
4. $7\text{s}$

Q. A bomb weighing $3.7\text{kg}$ is dropped from an aeroplane flying horizontally at $100{\text{ms}}^{-1}$. If the plane is $1\text{km}$ high, what is the horizontal distance that the bomb travels before reaching the ground?
(Take $g=10m/s^2$)

1. $37000\text{m}$
2. $3700\text{m}$
3. $37\times {10}^9\text{m}$
4. $1000\sqrt{2}\text{m}$

Q. A body of mass $m$ thrown horizontally with velocity $v$, from the top of a tower of height $h$ touches the level ground at a distance of $250\text{m}$ from the foot of the tower. A body of mass $2m$ thrown horizontally with velocity $\frac{v}{2}$ from the top of a tower of height $4h$ will touch the level ground at a distance $x$ from the foot of tower. The value of $x$ is

1. $250\text{m}$
2. $500\text{m}$
3. $125\text{m}$
4. $250\sqrt{2}\text{m}$

Q. A body is thrown with a velocity of $20m{s}^{-1}$ from a building of height $15m$. If the angle of projection is ${30}^{\circ }$ above the horizontal, the time of flight and the range of the projectile are respectively.
(Take $g=10m/s^2$)

1. $1s,30m$
2. $3s,30m$
3. $3s,30\sqrt{3}m$
4. $1s,30\sqrt{3}m$

Q. A body is projected horizontally with a velocity of $10\text{m/s}$ from the top of an inclined plane of angle ${45}^{\circ }.$ If the body hit the foot of the plane, the height of the plane (in $\text{m}$) is

1. $10\text{m}$
2. $20\text{m}$
3. $30\text{m}$
4. $40\text{m}$

Q. A body is projected horizontally with a velocity of $10\text{m/s}$ from the top of an inclined plane of angle ${45}^{\circ }$. If it is to hit the foot of the plane and acceleration due to gravity is $10m/s^2$, the height of the plane (in $\text{m}$ ) is

Q. A body is traveling down an inclined plane of angle of ${30}^{\circ }$ with an acceleration of $2m/s^2$, leaves it with speed of $20m/s$. If the inclined plane is located at a certain height above the ground, find its velocity when it travels in the horizontal direction after $1\text{second}$.

1. $11\sqrt{3}m/s$
2. $11\sqrt{2}m/s$
3. $10\sqrt{3}m/s$
4. $11m/s$