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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 

These particles A, B and C are projected from the same pair with same initial speed making angles ${30}^{o, }{45}^o \& {60}^o$ respectively with the horizontal. Which of the following statements is correct .
1. A, B and C have unequal ranges 
2. Range of A and C are less than that of B 
3. Range of A and C are equal & greater than that of B 
4. A, B and C have equal ranges  

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 body is projected with velocity u at an angle $\theta$ with horizontal from a moving cart then path of the body appears to be 

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

 
Two particles A and B are projected with velocity $u_{1}and u_2$ simultaneously. Time after which they start moving perpendicularly to each other is ?
$1. \frac{\sqrt{u_1{u}_2}}{g}$
$2. \frac{2\sqrt{u_1{u}_2}}{g}$
$3. \frac{\sqrt{u_1{u}_2}}{2g}$
$4. \frac{\sqrt{2u_1{u}_2}}{g}$
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