A particle is projected at an angle $\theta$ with horizontal with an initital speed u. When it makes and angle $\alpha$ with horizontal, its speed 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 body thrown vertically so as to reach its maximum height in t second. The toal time from the time of projection to reach a point at half of its maximum height while returning (in second) is:

(1) $\sqrt{2}t$

(2) $\left(1+\frac{1}{\sqrt{2}}\right)t$

(3) $\frac{3t}{2}$

(4) $\frac{t}{\sqrt{2}}$

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

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

 A body is thrown horizontally with a velocity $\sqrt{2gh}$ from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is:

(1) h

(2) $\frac{h}{2}$

(3) 2h

(4) $\frac{2h}{3}$

A body projected with velocity u with an angle of projection $\theta$. Change in velocity after the time (t) from the projection is:

(1) gt

(2) $\frac{1}{2}g{t}^2$

(3) u sin$\theta$

(4) u cos$\theta$

The gravity in space is given by $\overrightarrow{\mathrm{g}}=-10 \hat{j} m{s}^{-2}$. Two particles are simultaneously projected with velocity $\overrightarrow{{\mathrm{u}}_1}=\left(10 m{s}^{-1}\right)\hat{i}+\left(10 m{s}^{-1}\right)\hat{j}$ and $\overrightarrow{{\mathrm{u}}_2}=\left(20 m{s}^{-1}\right)\hat{i}+\left(10 m{s}^{-1}\right)\hat{j}$. Then, the ratio of their times of flight

1. 1:1

2. 1:2

3. 2:1

4. none