The Symmetry of the Path Traced

Q. A relief aeroplane is flying at a constant height of $1960\text{m}$ with $600\text{km/hr}$ speed above the ground towards a point directly over a person struggling in flood water. At what angle of sight with the vertical should the pilot release a survival kit if it has to reach the person in water ?
$(g=9.8{\text{m/s}}^2)$

1. ${30}^{\circ }$
2. ${37}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. A man projects a coin upwards from the gate of a uniformly moving train. The path of coin for the man will be

1. Parabolic
2. Inclined straight line
3. Vertical straight line

4. Horizontal straight line

Q. Two particals 1 &2 move with constant velocity v1 and v2 along two mutually perpendicular straight lines towards intersection point O. At a moment t=O the particals were located at the distance l1 and l2 from point o . How soon will the distance between two particals become the smallest? What it is equal to?

Q. A particle is projected with speed $u$ to just pass over a tower of height $h$. The product of the two possible times taken to pass over the tower is

1. None
2. $\frac{u}{g}$
3. $\frac{2h}{g}$
4. $\frac{2u}{g}$

Q. An aeroplane is observed by two persons travelling at 60km/h in two vehicles moving in opposite direction in a straight line road.To an observer in one vehicle the aeroplane appears to cross the road track at right angles while to the observer in other vehicle the angle appears to be 45 degree.At what angle does the plane actually cross the road track and what is its speed relative to the ground?

Q. A ball is thrown from a point with a speed $v_0$ at an elevation angle of $\theta$. From the same point and at the same instant, a person starts running with a constant speed $\frac{v_0}{2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection $\theta$ ?

1. No
2. $\text{yes},{30}^{\circ }$
3. $\text{yes},{60}^{\circ }$
4. $\text{yes},{45}^{\circ }$

Q. A water jet is being used to fill a cylindrical container of diameter $1m$ and height $2m$. The jet shoots the water at an angle of ${45}^o$ with velocity $u$ above the same horizontal plane on which the container is kept. The distance between the jet and container is $6m$ as shown in the diagram. For which of the following value(s) of $u$, the water will fill up the container. (Take $g=10m/s^2)$

1. $\sqrt{92}$
2. $\sqrt{67}$
3. $\sqrt{97}$
4. $\sqrt{62}$

Q. A girl thows a water filled balloon on the eve of Holi with a velocity 12 ms${}^{-1}$ at an angle of ${60}^{\circ }$ with the horizontal. It hits a car at the same height (of throw) approaching her at 15 ms${}^{-1}$. Find the initial distance of the car from her.

1. $13$ m
2. $18$ m
3. $31$ m
4. $44$ m

Q. For an observer on trolley, the direction of projection of particle is shown in figure, while for observer on ground ball rises vertically. Maximum height (in meter) seen from the trolley is:

(take $g=10{\text{ms}}^{-2}$)

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 $t_1$ 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. $\frac{R}{4g}$
2. $\frac{R}{g}$
3. $\frac{R}{2g}$
4. $\frac{2R}{g}$

Q. A stone is projected from the ground with velocity $50\text{m/s}$ at an angle of ${30}^{\circ }$. It crosses a wall after $3\text{sec}$. How far (approx) beyond the wall the stone will strike the ground ? $(g=10{\text{m/sec}}^2)$

Q. If the bob in a pendulum starts from x = +A at t=0, then, at the mean position of a simple pendulum, the values of velocity and acceleration will be

1. v= max and a=0
2. v= max and a=max
3. v= 0 and a=0
4. v= 0and a=max

Q. In a soccer practice session the ball is kept at the centre of the field $40$ yards from the $10ft$ high goal post . A goal is attempted by kicking the ball at a speed of $64ft/s$ at an angle of ${45}^0$ to the horizontal. Will the ball reach the goal post ?

Q. Particle is projected with speed $5\sqrt{2}\text{m/s}$ at an angle of projection ${45}^{\circ }$ from horizontal. At maximum height it breaks in two identical particle, velocity of one particle is zero, find out distance (in $\text{m}$) of second particle from point of projection when it hits ground. Take $g=10{\text{m/s}}^2$

Q. The greaest height to which a man can throw a stone is h. The greatest distance to which he can throw it, will be :

Q.

A particle moves in a plane with constant acceleration in a direction different from the initial velocity. The path of the particle will be

1. A straight line

2. An arc of a circle

3. A parabola

4. An ellipse

Q. A rod of rest length L moves at a relativistic speed. Let L' = L/γ. Its length

(a) must be equal to L'
(b) may be equal to L
(c) may be more than L' but less than L
(d) may be more than L

Q. Assertion :The time of flight 'T' is the sum of time of ascent and time of descent. Reason: The time of ascent is equal to the time of descent for a body thrown vertically up.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. A projectile is thrown at a speed of 20 m/s at an angle of ${53}^{\circ }$ with the horizontal. When it is at the highest point, its center of curvature is at $(g=10m/s^2)$

1. Ground
2. 1.2 m below ground
3. 1.6 m below ground
4. 2 m above ground

Q. A body is thrown with a velocity of $10m/s$ at an angle of ${45}^o$ to the horizontal. The radius of curvature of its trajectory in $t=1/\sqrt{2}$sec after the body began to move is:

1. $0m$
2. $2.5m$
3. $5m$
4. None

Q. Two bodies were thrown simultaneously from the same point, one straight up, and the other, at an angle of ${30}^o$ to the horizontal. The initial speed of each body is $20$ $m{s}^{-1}.$ Neglecting air resistance, the distance between the bodies at $t=1.2$ later

1. $20m$
2. $30m$
3. $24m$
4. $50m$

Q. A projectile is thrown at a speed of 20 m/s at an angle of ${53}^{\circ }$ with the horizontal. When it is at the highest point, its center of curvature is at $(g=10m/s^2)$

1. Ground
2. 1.6 m below ground
3. 2 m above ground
4. 1.2 m below ground

Q. Determine the height above the dashed line XX' attained by the water stream coming out through the hole is situated at point B in the diagram given. Given that $h=10$m, $L=2$m and $d={30}^o$.

1. $10$m
2. $7.1$m
3. $5$m
4. $3.2$m

Q. Projectile A is thrown horizontaly from tower of height H and projectile B is thrown from the ground at an angle $\theta$ as shown in the figure. During the duration when both are in air,

1. Path of A as seen by B will be a straight line
2. Path of A as seen by B will be a parabola
3. Motion of A is uniformly accelerated as seen by B.
4. Relative acceleration of A with respect to B is zero

Q. A particle is projected from ground at angle ${45}^{\circ }$ with initial velocity $20\sqrt{2}m/s.$ Find magnitude of average velocity in a time interval from $t=0$ to $t=3s$. Round off to the nearest integer.

Q. A water jet is being used to fill a cylindrical container of diameter $1m$ and height $2m$. The jet shoots the water at an angle of ${45}^o$ with velocity $u$ above the same horizontal plane on which the container is kept. The distance between the jet and container is $6m$ as shown in the diagram. For which of the following value(s) of $u$, the water will fill up the container. (Take $g=10m/s^2)$

1. $\sqrt{92}$
2. $\sqrt{67}$
3. $\sqrt{97}$
4. $\sqrt{62}$

Q. A projectile is thrown in to space so as to have the maximum possible horizontal range equal to $400m$. Taking the point of projection as the origin, the coordinate of the point where the velocity of the projectile is minimum are

1. $(400,200)$
2. $(200,200)$
3. $(400,100)$
4. $(200,100)$

Q. A projectile is thrown at a speed of 20 m/s at an angle of ${53}^{\circ }$ with the horizontal. When it is at the highest point, its center of curvature is at $(g=10m/s^2)$

1. Ground
2. 1.6 m below ground
3. 2 m above ground
4. 1.2 m below ground

Q. Why is the following situation impossible? The object of mass $m=4.00kg$ in below figure is attached to a vertical rod by two strings of length, $l=2.00m$. The strings are attached to the rod at points a distance $d=3.00m$ apart. The object rotates in a horizontal circle at a constant speed of $v=3.00m/s$, and the strings remain taut. The rod rotates along with the object so that the strings do not wrap onto the rod. What If? Could this situation be possible on another planet.

Q. A water jet is being used to fill a cylindrical container of diameter $1m$ and height $2m$. The jet shoots the water at an angle of ${45}^o$ with velocity $u$ above the same horizontal plane on which the container is kept. The distance between the jet and container is $6m$ as shown in the diagram. For which of the following value(s) of $u$, the water will fill up the container. (Take $g=10m/s^2)$

1. $\sqrt{92}$
2. $\sqrt{67}$
3. $\sqrt{97}$
4. $\sqrt{62}$