Projectile from a Height

Q.

A stone is thrown in a vertically upward direction with a velocity of $5m{s}^{-1}$. If the acceleration of the stone during its motion is $10m{s}^{-2}$ in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?

Q.

An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

1. 1200 m

2. 0.33 km

3. 3.33 km

4. 33 km

Q. A body falls from a height '$h$' on a horizontal surface and rebounds. Then it falls again and rebounds and so on. If the coefficient of restitution is $\frac{1}{2}$, then the total distance travelled by the ball before coming to rest is (neglect air resistance)

1. $\frac{2h}{3}$
2. $\frac{3h}{2}$
3. $\frac{5h}{2}$
4. $\frac{5h}{3}$

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. A particle $A$ is dropped from a height and another particle $B$ is projected in horizontal direction with speed of $5m/s$ from the same height, then correct statement is

1. particle $B$ will reach at ground first with respect to particle $A$
2. both particles will reach at ground simultaneously.
3. both particles will reach at ground with same speed.
4. particle $A$ will reach at ground first with respect to particle $B$.

Q.

A bullet is dropped from the same height when another bullet is fired horizontally. They will hit the ground

1. One after the other

2. Simultaneously

3. Depends on the observer

4. None of the above

Q. A boat is moving towards east with velocity $4\text{m/s}$ with respect to river flowing towards north with velocity $2\text{m/s}$ and the wind is blowing towards north with velocity $6\text{m/s}$. The direction of the flag blown over by the wind hoisted on the boat is

1. North-west
2. South-east
3. ${\tan }^{-1}(\frac{1}{2})$ with east
   
4. North

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. From the top of a $11\text{m}$ high tower a stone is projected with speed $10\text{m/s}$, at an angle of ${37}^{\circ }$ as shown in the figure. (Take $g=10m/s^2$)


Match the quantities in column-I to their values in column-II

Column-I	Column-II
(i) Speed after $2\text{s}$	p. $8\sqrt{5}$
(ii)Time of flight	q. $12.8$
(iii)Range	r. $\frac{11}{5}$
(iv) The maximum height attained by the stone	s. $\frac{88}{5}$
(v) Speed just before striking the ground.	t. $\sqrt{260}$

1. (i) - p, (ii) - t, (iii) - s, (iv) - q, (v) - r
2. (i) - t, (ii) - r, (iii) - s, (iv) - q, (v) - p
3. (i) - p, (ii) - r, (iii) - s, (iv) - q, (v) - t
4. (i) - r, (ii) - s, (iii) - p, (iv) - q, (v) - t

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. 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 rolls off the top of a stairway horizontally with a velocity of $4.5{\text{ms}}^{-1}$. Each step is $0.2\text{m}$ high and $0.3\text{m}$ wide. If $g$ is $10{\text{ms}}^{-2}$, then the ball will strike the $n^{th}$ step where $n$ is equal to

1. $3$
2. $9$
3. $2$
4. $4$

Q. A ball is projected horizontally with a speed $v$ from the top of a plane inclined at an angle ${45}^{\circ }$ with the horizontal. How far from the point of projection will the ball strike the plane?

1. $\frac{v^2}{g}$
2. $\sqrt{2}\frac{v^2}{g}$
3. $\frac{2v^2}{g}$
4. $\sqrt{2}\left[\frac{2v^2}{g}\right]$

Q.

A particle is projected vertically upwards with a velocity of 20 m/sec. Find the time at which the distance travelled is twice the displacement

1. $2+\sqrt{\frac{4}{3}}sec$

2. 1 sec

3. 3 sec

4. $2+\sqrt{\frac{3}{4}}$

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 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 projectile is thrown horizontally with a speed of $20{\text{m s}}^{-1}$. If $g$ is $10{\text{ms}}^{-2}$, then the speed of the projectile after $5$ seconds will be nearly

1. $0.5{\text{ms}}^{-1}$
2. $54{\text{ms}}^{-1}$
3. $5{\text{ms}}^{-1}$
4. $500{\text{ms}}^{-1}$

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

1. Slower one
2. Faster one
3. Both will reach simultaneously
4. It cannot be predicted

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 bomb is dropped from an aeroplane flying horizontally with a velocity $469{\text{ms}}^{-1}$ at an altitude of $980\text{m}$. The bomb will hit the ground after a time

$(g=9.8{\text{m/s}}^2)$

1. $2\text{s}$
2. $\sqrt{2}\text{s}$
3. $5\sqrt{2}\text{s}$
4. $10\sqrt{2}\text{s}$

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 boy standing on a building of height $20\text{m}$ throws a stone with a velocity of $15{\text{ms}}^{-1}$. What should be the angle of projection so that the stone has a range of $30\text{m}$ ?
(Take $g=10m/s^2$)

1. ${\tan }^{-1}\frac{3}{2}$
2. ${\tan }^{-1}\frac{3}{4}$
3. ${30}^{\circ }$
4. ${45}^{\circ }$

Q. A boy playing on the roof of a $10m$ high building throws a ball with a speed of $10m/s$ at an angle of ${30}^{\circ }$ with the horizontal. The time taken by the ball to cross the point which is at the height of $10m$ from the ground is

1. $1s$
2. $2s$
3. $3s$
4. $4s$

Q. A ball was thrown from height $H$ and the ball hits the floor with velocity $10(\hat{i}-\hat{j})\text{m/s},$ $1.5$ sec after its projection. Find initial speed of ball.

1. $10\sqrt{5}\text{m/s}$
2. $5\sqrt{5}\text{m/s}$
3. $15\text{m/s}$
4. $30\text{m/s}$

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. 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. Two particles are projected from the top of a tower with velocities $10\text{m/s}$ and $80\text{m/s}$ in horizontal but in opposite directions. After what time $t$ their velocity vectors will be mutually perpendicular to each other? (Take $g=10{\text{m/s}}^2$)

1. $2\sqrt{2}\text{sec}$
2. $2\text{sec}$
3. $4\text{sec}$
4. $8\text{sec}$

Q.

An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth's surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling

1. On a parabolic path as seen by pilot in the plane

2. Vertically along a straight path as seen by an observer on the ground near the target

3. On a parabolic path as seen by an observer on the ground near the target

4. On a zig-zag path as seen by pilot in the plane

Q. Two tall buildings are $40\text{m}$ apart. With what speed a ball must be thrown horizontally from a window $145\text{m}$ above the ground in one building, so that it will enter a window $22.5\text{m}$ above the ground in the other ?
(Take $g=10m/s^2$)

1. $5{\text{ms}}^{-1}$
2. $8{\text{ms}}^{-1}$
3. $10{\text{ms}}^{-1}$
4. $16{\text{ms}}^{-1}$