Time of Flight

Q. A helicopter rises from rest on the ground vertically upwards with a constant acceleration $g$. A food packet is dropped from the helicopter when it is at a height $h$. The time taken by the packet to reach the ground is close to

[$g$ is the acceleration due to gravity]

1. $t=\frac{2}{3}\sqrt{\left(\frac{h}{g}\right)}$
2. $t=1.8\sqrt{\frac{h}{g}}$
3. $t=3.4\sqrt{\left(\frac{h}{g}\right)}$
4. $t=\sqrt{\frac{2h}{3g}}$

Q. A particle is projected from the ground with an initial speed $u$ at an angle $\theta$ with horizontal. The average velocity of the particle between its point of projection and the highest point of its trajectory is

1. $\frac{u}{2}\sqrt{1+{\cos }^2\theta }$
2. $\frac{u}{2}\sqrt{1+2{\cos }^2\theta }$
3. $\frac{u}{2}\sqrt{1+3{\cos }^2\theta }$
4. $\frac{u}{2}\sqrt{1+4{\cos }^2\theta }$

Q.

If for a given angle of projection, the horizontal range is doubled, the time of flight becomes

1. 

2. 

3. 

4. 

Q. A uniform meter stick is held vertically with one end on the floor and is allowed to topple such that the end at the floor does not slip. The speed of the other end, when it hits the floor, will be -

1. $\sqrt{4g}$
2. $\sqrt{3g}$
3. $\sqrt{5g}$
4. $\sqrt{g}$

Q. A ball is thrown horizontally from the top of a tower of unknown height. The ball strikes a vertical wall whose plane is normal to the plane of motion of the ball. The collision is elastic and the ball falls on the ground exactly at the midpoint between the tower and the wall. The ball strikes the ground at an angle ${30}^{\circ }$ with the horizontal. Find the height of the tower (in meters).

Q. A football player throws a ball with a velocity of 50 metre/sec at an angle 30 degrees from the horizontal. The ball remains in the air for $(g=10m/s^2)$

1. 5 sec
2. 0.625 sec
3. 2.5 sec
4. 1.25 sec

Q. A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1\text{and}{t}_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1{t}_2$ is :

1. $\frac{2R}{g}$
2. $\frac{R}{g}$
3. $\frac{R}{2g}$
4. $\frac{R}{4g}$

Q.

A body is thrown with a velocity of 9.8 m/s making an angle of ${30}^{\circ }$ with the horizontal. It will hit the ground after a time

1. 1.5 s

2. 1 s

3. 3 s

4. 2 s

Q. A body is thrown vertically upwards with velocity u. The distance travelled by it in the fifth and the sixth seconds are equal. The velocity u is given by (g=9.8 m/$s^2)$

1. 98.0 m/s
2. 24.5 m/s
3. 49.0 m/s
4. 73.5 m/s

Q. In the figure shown, a particle is released from position $\text{A}$ on a smooth track, when the particle reaches $\text{B}$, then the velocity of the particle is

1. $2\sqrt{gh}$
2. $\sqrt{gh}$
3. $\sqrt{3gh}$
4. $\sqrt{2gh}$

Q. A projectile is thrown from the ground with an initial velocity of $(4\hat{i}+3\hat{j})$$m/s$. It reaches its greatest height above the ground after (Take $g=10m/s^2$)

1. $0.20s$
2. $0.30s$
3. $0.45s$
4. $4.5s$

Q.

Neglecting the air resistance, the time of flight of a projectile is determined by

1. $U_{horizontal}$

2. $U=U_{vertical}^2+U_{horizontal}^2$

3. $U=U(U_{vertical}^2+U_{horizontal}^2{)}^{\frac{1}{2}}$

4. $U_{vertical}$

Q. A boy can throw a stone up to a maximum height of $10\text{m}$. The maximum horizontal distance that the boy can throw the same stone up to will be

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

Q.

The friction of the air causes vertical retardation equal to one tenth of the acceleration due to gravity (Take g = $10m{s}^{-2}$). The time of flight will be decreased by

1. 

2. 

3. 

4. 

Q. In case of projectile motion if two projectiles A and B are projected with same speed at angles ${15}^{\circ }$ and ${75}^{\circ }$ respectively to the horizontal then:

1. $H_A=H_B$
2. $H_A<H_B$
3. $T_A=T_B$
4. $T_A<T_B$

Q. A stone is projected at an angle ${45}^{\circ }$ to the horizontal with a velocity $12\sqrt{g}$, where $g$ is acceleration due to gravity at the place. It just passes over a wall $27\text{m}$ high, at a horizontal distance of $108\text{m}$ from the point of projection. Take $g=10{\text{ms}}^{-2}$

1. The stone passes over the wall during ascent.
2. The stone passes over the wall during descent.
3. The difference in velocity at the initial and final point on ground is zero.
4. The difference in speed at the initial and final point on ground is zero.

Q. Two projectiles $\text{A}$ and $\text{B}$ are thrown with the same speed such that $\text{A}$ makes angle $\theta$ with the horizontal and $\text{B}$ makes angle $\theta$ with the vertical, then -

1. Both must have same time of flight
2. Both must achieve same maximum height
3. $\text{A}$ must have more horizontal range than $\text{B}$
4. Both may have same time of flight

Q.

A particle is thrown with velocity u at an angle $\alpha$ from the horizontal. Another particle is thrown with the same velocity at an angle $\alpha$ from the vertical. The ratio of times of flight of two particles will be

1. 

2. 

3. 

4. 

Q. A small body is dropped from a rising balloon. A person $\text{A}$ stands on the ground, while another person $\text{B}$ is on the balloon. Choose the correct statement, immediately after the body is released.

1. $\text{A}$ and $\text{B}$, both feel that the body is coming (going) down.
2. $\text{A}$ and $\text{B}$, both feel that the body is going up.
3. $\text{A}$ feels that the body is coming down, while $\text{B}$ feels that the body is going up.
4. $\text{A}$ feels that the body is going up, while $\text{B}$ feels that the body is stationary.

Q.

A ball thrown by a boy is caught by another after 2 sec. some distance away in the same level. If the angle of projection is ${30}^{\circ }$, the velocity of projection is

1. None of these

2. 19.6 m/s

3. 9.8 m/s

4. 14.7 m/s

Q. Two masses $m$ and $2m$ are at rest initially. Find the velocity of mass $2m$, when their separation reduces to $\frac{d}{2}$ due to gravitational force of attraction.

1. $\sqrt{\frac{Gm}{2d}}$
2. $\sqrt{\frac{Gm}{d}}$
3. $\sqrt{\frac{2Gm}{3d}}$
4. $\sqrt{\frac{Gm}{3d}}$

Q. A body is projected vertically upwards with a speed of $\sqrt{\frac{GM}{R}}$. The body will attain a height of
$(M$ is mass and $R$ is Radius of earth$)$

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

Q. Pankaj and Sudhir are playing with two different balls of masses m and 2m respectively. If Pankaj throws his ball vertically up and Sudhir at an angle $\theta$ with the vertical, both of them stay in our view for the same period. The height attained by the two balls are in the ratio

1. 
2. 
3. 
4. 

Q.

The maximum height reached by the projectile is $4m$. The horizontal range is $12m$. The velocity of projection in $m{s}^{-1}$ Is (g - acceleration due to gravity)

Q. A cannon $B$ and a target are $0.98\text{km}$ apart located at the same level. Find the time taken to hit the target, if the speed of the shell fired by the cannon is $98\text{m/s}$. Neglect the air drag and take $g=9.8{\text{m/s}}^2$.

1. $10\sqrt{3}\text{s}$
2. $10\text{s}$
3. $10\sqrt{2}\text{s}$
4. $20\sqrt{2}\text{s}$

Q. A particle (A) is dropped from a height and another particle (B) is thrown in horizontal direction with speed of 5 m/sec from the same height. The correct statement is

1. Both particles will reach at ground simultaneously
2. Both particles will reach at ground with same speed
3. Particle (A) will reach at ground first with respect to particle (B)
4. Particle (B) will reach at ground first with respect to particle (A)

Q.

At what angle should a projectile with initial velocity v be thrown, so that it achieves its maximum range?

Q. A body is thrown with a velocity $9.8m{s}^{-1}$ making an angle of ${30}^{\circ }$ with the horizontal. It will hit the ground after a time.

1. $3.0s$
2. $2.0s$
3. $1s$
4. $1.5s$

Q. Two stones $A$ and $B$ are projected from the same point. $B$ is thrown $1$ second after $A$ is thrown. $A$ is projected with a velocity of $60m/s$ at an angle ${30}^{\circ }$ with the horizontal and $B$ is projected with velocity $u$ at an angle of ${45}^{\circ }$ with the horizontal. Find $u$ if both stones hit the ground at the same time. (Take $g=10m/s$)

1. $25m/s$
2. $25\sqrt{2}m/s$
3. $25\sqrt{3}m/s$
4. $\frac{25}{2}m/s$

Q. Referring to above question, the angle with the horizontal at which the projectile was projected is

1. $ta{n}^{-1}\left(\frac{3}{4}\right)$
2. $ta{n}^{-1}\left(\frac{4}{3}\right)$
3. $Notobtainablefromthegivendata$
4. $si{n}^{-1}\left(\frac{3}{4}\right)$