Intro to Relative Projectile

Q. A stone projected with a velocity $u$ at an angle $\theta$ with the horizontal reaches maximum height $H_1$. When it is projected with velocity $u$ at an angle $(\frac{\pi }{2}-\theta )$ with the horizontal, it reaches the maximum height $H_2$. The relation between the horizontal range $R$ of the projectile, $H_1$ and $H_2$ is

1. $R=4\sqrt{H_1{H}_2}$
2. $R=4(H_1-H_2)$
3. $R=4(H_1+H_2)$
4. $R=\frac{H_1^2}{H_2^2}$

Q. Two particles are projected simultaneously in the same vertical plane, from the same point, but with different speeds and at different angles to the horizontal. The path followed by one, as seen by the other, till both are in air is

1. A vertical straight line
2. A straight line making a constant angle $(\ne {90}^{\circ })$ with the horizontal
3. A hyperbola
4. A parabola

Q.

A particle is projected with an initial speed u form a point at height h above the horizontal plane as shown is the fig. Find the maximum range on the horizontal plane

1. $u\sqrt{\frac{u^2+2gh}{g}}$

2. $u\frac{\sqrt{2gh}}{g}$

3. $\frac{u}{g}\sqrt{u^2+2gh}$

4. $\sqrt{\frac{u^2+2gh}{g}}$

Q.

A particle is projected vertically upwards from $O$ with velocity $v$ and a second particle is projected at the same instant from $P$ (at a height h above $O$) with velocity $v$ at an angle of projection $\theta$. The time when the distance between them is minimum is

1. 

2. 

3. 

4. 

Q.

In the above problem, given that $M_2=2M_{1}and{M}_2$ moves vertically downwards with acceleration a. If the position of the masses are reversed the acceleration of $M_2$ down the inclined plane will be

1. 

2. 

3. 

4. 

Q.

A particle is projected from point A on the ground at an angle $\theta$ with horizontal. Another particle is projected from point B simultaneously from height 4H above point A with same velocity. A and B are in the same vertical plane, where H is the maximum height attained by the particle A. Both the particles collide at the same time on the ground. Find the angle at which particle B is projected with horizontal:

1. Zero

2. θ upwards

3. θ downwards

4. 2θ upwards

Q.

A projectile has a range R and time of flight T. If the range is doubled by increasing the speed of projection, without changing the angle of projection, the time of flight will become

1. $\frac{T}{\sqrt{2}}$

2. $\sqrt{2}T$

3. $\frac{T}{2}$

4. $2T$

Q. A stone projected with a velocity with a velocity $u$ at an angle $\theta$ with the horizontal reaches maximum height $H_1$. When it is projected with the velocity $u$ at an angle $(\frac{\pi }{2}-\theta )$ with the horizontal, it reaches maximum height $H_2$. The relation between the horizontal range $R$ of the projectile, heights $H_1$ and $H_2$ is

1. $R=4\sqrt{H_1{H}_2}$
2. $R=4(H_1-H_2)$
3. $R=4(H_1+H_2)$
4. $R=\frac{H_1^2}{H_2^2}$

Q. A projectile thrown at an angle of ${30}^o$ with the horizontal has a range $R_1$ and attains a maximum height $h_1$ . Another projectile thrown, with the same speed, at an angle ${30}^o$ with the vertical, has a range $R_2$ and attains a maximum height $h_2$ . The relation between $R_1$ and $R_2$ is :-

Q. From the top of a building, a particle is projected up at an angle $\theta$ with horizontal and reaches the ground in time $t_1$. A second particle projected down at an angle $\theta$ with horizontal and with same speed reaches the ground in time $t_2$. If third particle projected horizontally with same speed reaches the ground in time $t_3$, then

1. $t_3=\sqrt{t_1{t}_2}$
2. $t_3=\frac{t_1+t_2}{2}$
3. $\frac{2}{t_3}=\frac{1}{t_1}+\frac{1}{t_2}$
4. $t_3=\sqrt{t_1^2+t_2^2}$

Q. The horizontal range of a projectile is maximum for a given velocity of projection when the angle of projection is :

1. ${60}^o$
2. ${30}^o$
3. ${90}^o$
4. ${45}^o$

Q. The range of a projectile at an angle $\theta$ is equal to half of the maximum range if thrown at the same speed. The angle of projection is given by

1. ${15}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. Data insufficient

Q. A fighter plane flying horizontal at an altitude of 1.5 Km with speed of 720 Km $h^{-1}$ passes directly overhead an anticarft gun. At what angle from the vertical should the gun be fired from the shell with muzzle speed 400 $m{s}^{-1}$ to hit the plane in shortest time.?

1. 8
   
2. 14.47
3. 6
4. 7

Q.

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles ${\theta }_1$ and ${\theta }_2$ respectively from the horizontal, then answer the following questions: If $v_1$ = $v_2$ and ${\theta }_1>{\theta }_2$, then choose the incorrect statement

1. Particle 2 moves under the particle 1

2. The slope of the trajectory of particle 2 with respect to 1 is always positive

3. Both the particles will have the same range if and and =

4. none of these

Q. In the figure shown, blocks A and B move with velocities $v_1$ and $v_2$ along horizontal direction. Find the ratio of $\frac{v_1}{v_2}$

Q.

Two particle A and B are moving with uniform velocity as shown in the figure given below at t =0.
I. Will the two particle collide
II. Find out shortest distance between two particles

1. 1

2. 2

3. 3

4. 4

Q.

Two particle A and B are moving with uniform velocity as shown in the figure given below at t =0.
I. Will the two particle collide
II. Find out shortest distance between two particles

1. 3

2. 4

3. 1

4. 2

Q. For proper water drainage from roof of building, pipes are used. One of the pipes, is shown in the figure. Height of the building is 20 m. Water strikes the ground at a horizontal distance of 8 m from the pipe opening. The speed of water as it leaves the pipe is (g = 10 m/s²)

ईमारत की छत से उचित जलनिकासी के लिए, पाइपों का उपयोग किया जाता है। चित्र में इनमें से एक पाईप दर्शाया गया है। ईमारत की ऊँचाई 20 m है। जल, पाइप के अग्र भाग से 8 m की क्षैतिज दूरी पर धरातल से टकराता है। जैसे ही जल पाइप से निकलता है, इसकी चाल है (g = 10 m/s²)

1. 8 m/s
2. 4 m/s
3. 2 m/s
4. 1.5 m/s

Q. The time of flight of a projectile on an upward inclined plane depends upon

1. the value of acceleration due to gravity
2. angle of projection
3. angle of inclination of the plane
4. all the above

Q.

A particle is projected vertically upwards from $O$ with velocity $v$ and a second particle is projected at the same instant from $P$ (at a height h above $O$) with velocity $v$ at an angle of projection $\theta$. The time when the distance between them is minimum is

1. $\frac{h}{2vsin\theta }$

2. $\frac{h}{2vcos\theta }$

3. $\frac{h}{v}$

4. $\frac{h}{2v}$

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

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

Q. If $h_1,h_2$ and $h_3$ are the displacements of object along the incline plane between $1st-2nd,2nd-3rd$ and $3rd-4th$ impact, then $h_1:h_2:h_3$.

Q. The range of a projectile for a given initial velocity is maximum when the angle of projection is $45$.The range will be minimum, if the angle of projection is:

1. 90
2. 180
3. 60
4. 75

Q. $R$ is the horizontal range of a projectile, fired with a certain speed at a certain angle with the horizontal, on a horizontal plane and $h$ is the maximum height attained by it. Then the maximum horizontal range that can be attained with the same speed of projection as before is:-

1. $2h$
2. $\frac{R^2}{8h}$
3. $2R+\frac{h^2}{8R}$
4. $2h+\frac{R^2}{8h}$

Q. One second after projection, a stone moves at an angle $45$ with horizontal. Two seconds after projection, it moves horizontally, its angle of projection is- $[$$g=10m/s^2$$]$

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

Q.

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles ${\theta }_1$ and ${\theta }_2$ respectively from the horizontal, then answer the following questions: If $v_1$ = $v_2$ and ${\theta }_1>{\theta }_2$, then choose the incorrect statement

1. Particle 2 moves under the particle 1

2. The slope of the trajectory of particle 2 with respect to 1 is always positive

3. Both the particles will have the same range if ${\theta }_1>{45}^{\circ }$ and ${\theta }_2<{45}^{\circ }$ and ${\theta }_1+{\theta }_2$ = ${90}^{\circ }$

4. none of these

Q. A block slide down an inclined plane (angle of inclination${60}^0$) with an acceleration g/2. Find the coefficient of kinetic (dynamic) friction.

Q. A vessel, whose bottom has round holes with diameter of 0.1 mm, is filled with water. The maximum height to which the water can be filled without leakage is-
(S.T of water $=75dyne/cm,g=1000cm/s^2$)

1. 100 cm
2. 75 cm
3. 50 cm
4. 30 cm

Q. Three projectile $A,B$ and $C$ are thrown simultaneously from the same point in the same vertical plane. Their trajectories are shown in the figure. Then which of the following statement is false?

1. The launch speed is greatest for particle $C$
2. The vertical velocity component for particle $C$ is greater than that for the other particles
3. The time of flight is the same for the three
4. Y-coordinate of all particle is always same