A ball rolls off top of a staircase with a horizontal velocity u $\mathrm{m}/\mathrm{s}$. If the steps are h metre high and b mere wide, the ball will just hit the edge of nth step if n equals to

1. $\frac{h{u}^2}{g{b}^2}$

2. $\frac{u^{2}8}{g{b}^2}$

3. $\frac{2h{u}^2}{g{b}^2}$

4. $\frac{2u^{2}g}{h{b}^2}$

A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity u. The ratio of their velocities when they reach the earth’s surface will be

1. $\sqrt{2gh+u^2} :u$

2. 1:2

3. 1:1

4. $\sqrt{2gh+u^2} :\sqrt{2gh}$

A particle is projected at an angle $\theta$ with horizontal with an initital speed u. When it makes an angle $\alpha$ with horizontal, its speed v is-

1. $u\cos \theta$

2. $u\cos \theta u\cos \alpha$

3. $\frac{u\sin \theta }{\sin \alpha }$

4. $\frac{u\cos \theta }{\cos \alpha }$

A body is projected with velocity $20\sqrt{3}$ m/s with an angle of projection 60$°$ with horizontal. Calculate velocity on that point where body makes an angle 30$°$ with the horizontal.

1. 20 m/s

2. $\frac{20}{\sqrt{3}} m/s$

3. $10\sqrt{3} m/s$

4. 10 m/s

A particle is moving with veocity $\stackrel{\rightharpoonup }{\mathrm{V}}=k(y\hat{i}+x\hat{j})$; where k is constant. The general equation for path is:

1. $\mathrm{y}={\mathrm{x}}^2+\mathrm{constant}$

2. ${\mathrm{y}}^2={\mathrm{x}}^2+\mathrm{constant}$

3. $\mathrm{y}=\mathrm{x}+\mathrm{constant}$

4. xy=constant

A particle is projected with a velocity u making an angle $\mathrm{\theta }$ with the horizontal. At any instant, its velocity v is at right angles to its initial velocity u; then v is:

1.  u cos $\mathrm{\theta }$

2.  u tan $\mathrm{\theta }$

3.  u cot $\mathrm{\theta }$

4.  u sec $\mathrm{\theta }$

A projectile is given an initial velocity of $\hat{i}+2\hat{j}$. The cartesian equation of its path is (g = 10 ${\mathrm{ms}}^{-2}$) 

1. $\mathrm{y}=2\mathrm{x}-5{\mathrm{x}}^2$

2. $\mathrm{y}=\mathrm{x}-5{\mathrm{x}}^2$

3. $4\mathrm{y}=2\mathrm{x}-5{\mathrm{x}}^2$

4. $\mathrm{y}=2\mathrm{x}-25{\mathrm{x}}^2$

A ship A is moving westwards with a speed of 10 km ${\mathrm{h}}^{-1}$ and a ship B, 100 km south of A is moving northwards with a speed of 10 km ${\mathrm{h}}^{-1}$. The time after which the distance between them becomes the shortest, is:

1. 5 hr

2. $5\sqrt{2}$ hr

3. $10\sqrt{2}$ hr

4. 0 hr

Time taken by the projectile to reach from A to B is t. Then the distance AB is equal to :

1. $\frac{ut}{\sqrt{3}}$

2. $\frac{\sqrt{3}ut}{2}$

3. $\sqrt{3}ut$

4. 2ut

A particle projected with kinetic energy ${\mathrm{k}}_0$ with an angle of projection $\mathrm{\theta }$. Then the variation of kinetic K with vertical displacement y is

1.  linear

2.  parabolic

3.  hyperbolic

4.  periodic