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If horizontal range of a projectile is 4$\sqrt{3}$ times its maximum height. Its range of projection will be
1. $45°$
2. $60°$
3. $90°$
4. $30°$

A stone is pfojected with a velocity v at an angle $\theta$ with the horizontal reaches maximum height H₁. When it is projected with u at an angle $\left(\frac{\mathrm{\pi }}{2}-\theta \right)$ with the horizontal, it reaches maximum height H₂. The ratio between hrizontal range  R of the projection, H₁ and H₂ is ?
1. $R = 2\sqrt{H_1{H}_2}$
2. $R = \sqrt{H_1{H}_2}$
3. $R = 4\sqrt{H_1{H}_2}$
4. $R = 8\sqrt{H_1{H}_2}$

The velocity of a projectile at the initial point A is $\left(4\hat{i}+5\hat{j}\right)$ m/s. Its velocity in m/s at point B is

1. $\left(4\hat{i}+5\hat{j}\right)$
2. $\left(-4\hat{i}-5\hat{j}\right)$
3. $\left(-4\hat{i}+5\hat{j}\right)$
4. $\left(4\hat{i}-5\hat{j}\right)$

A body is projected with initial kinetic energy of 100 J and at an angle of $60°$ with the horizontal. The K.E. of the body at highest point will be
1. 25 J
2. 50 J
3. 75 J
4. 0 J

The equation of trajectory of a projectile given angular projection is y = ax - bx², then horizontal range of projectile is 
1. $\frac{a}{b}$
2. $\frac{a}{2b}$
3. $\frac{2a}{b}$
4. $\frac{a}{4b}$

A large number of bullets are fired in all directions with same velocity u. What is the maximum area on the ground on which these bullets can spread ?
1. $\frac{{\mathrm{\pi u}}^2}{g}$
2. $\frac{{\mathrm{\pi u}}^4}{g^2}$
3. $\frac{{\pi }^2{u}^4}{g^2}$
4. $\frac{{\pi }^2{u}^2}{g^2}$

A particle is thown with a speed u at an angle $\theta$ with the horizontal. When the particle makes an angle $\varphi$ with the horizontal, its speed changes to v, Which is equal to 
1. $u \cos \theta$
2. $u \cos \theta \cos \varphi$
3. $u \cos \theta sec \varphi$
4. $u sec \theta \cos \varphi$

A smooth square platform ABCD is moving towards right with uniform speed u. At what angle $\theta$ must a particle be projected from A with speed v, so that it strikes the point D ?

1. ${\sin }^{-1}\left(\frac{u}{v}\right)$
2. ${\cos }^{-1}\left(\frac{v}{u}\right)$
3. ${\sin }^{-1}\left(\frac{v}{u}\right)$
4. ${\cos }^{-1}\left(\frac{u}{v}\right)$

Time taken by the projectile to reach from P to Q is t, then PQ ?
1.  2ut
2. $\sqrt{3 }ut$
3. $\frac{\sqrt{3}}{2}ut$
4. $\frac{ut}{\sqrt{3}}$

A aeroplane moving with a speed of 250m/s is at a height of 6000 m just overhead of an ant, aircraft gun. Muzzle speed of shell is 500m/s, the firing angle $\theta$ should be ?

1. ${45}^0$
2. ${60}^0$
3. ${30}^0$
4. None
 

The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y=8t-5t^2 m$ and x = 6t m, where t is in seconds. The velocity with which the particle is projected is.
1. 14 m/s
2. 10 m/s
3. 8 m/s 
4. 6 m/s

A particle of mass m is projectile with a velocity v making an angle of ${30}^o$ with the horizontal. The magnitude of angular momentum of the projectile about the point of the projection when particle is at it's maximum height h is 
$1. \sqrt{\frac{3}{2}}\frac{m{v}^2}{g}$
$2. zero$
$3. \frac{m{v}^3}{\sqrt{2}g}$
$4. \frac{\sqrt[]{}3}{16}\frac{m{v}^3}{g}$

if a person can through a stone to maximum height of h meter vertically, then maximum distance through which it can be thrown horizontally by the same person is 
1. h/2
2. h
3. 2h
4. 3h
 

At the top of the trajectory of a projectile, direction of its velocity and acceleration are 
1. perpendicular to each other 
2. parallel to each other 
3. inclined to each other at angle of ${45}^0$
4. antiparallel to each other 

At the height 80 m an aeroplane is moving with 150m/s. A bomb is dropped from it, so as to hit a target. At what distance from the target should bomb be dropped ?
1. 605.3 m
2. 600 m
3. 80 m
4. 230 m 

Three balls are dropped from the top of a building with equal speed at different angles. When the balls strike the ground, their velocities are ${}_{}$\(v_1,v_2\) and \(v_3\) respectively, then:
1. \( v_{1} > v_{2} > v_{3}\)
2. \(v_{3}   > v_{2} >   v_{1}\)
3. \(  v_{1  } =   v_{2} =   v_{3}\)
4. \(v_{1}   < v_{2}   < v_{3}\)
${\mathrm{}}_{}$

An object of mass 2m is projected with a speed of 100 m/s at an angle $\theta = {\sin }^{-1}\left(\frac{3}{5}\right)$ to the horizontal. At the highest point, the object breaks into pieces of same mass m & the first one comes to rest . The distance between point of landing of the bigger piece is (given g = 10 m/s² )
1. 3840 m
2. 1280 m
3. 1440 m
4. 960 m

A cart is moving horizontally along a straight line with contant speed of 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80 m. At what speed (relative to the cart) must the projectile be fired ? (given g = 10 m/s²)
1. 10 m/s
2. $\frac{40}{3} m/s$
3. $10\sqrt{8} m/s$
4. None of the above 

A cart is moving with speed of 20m/s on a horizontal track. A body is projected with speed 40m/s (relative to cart ) from the cart in such a way that path of body appear to be straight line for an observer on ground. Time for which body remains in air is:
$1. 2\sqrt{3} sec$
$2. 4 sec$
$3. 4\sqrt{3 }sec$
$4. 8 sec$
 

A body is projected with speed u at an angle $\theta$ with the horizontal after what time it will start moving perpendicular to its initial direction of projection.
1. $t = \frac{u}{g \sin 2\theta }$
2. $t = \frac{2u}{g \sin \theta }$
3. $t = \frac{u}{2g \sin \theta }$
4. $t = \frac{u}{g \sin \theta }$