A man starts from point 'P' and goes 20 m due East, then 5 m due North, then 35 m due West, and finally 25 m due South. His displacement from point 'P' is:

1.	25 m at \(\tan^{-1}(\frac{4}{3})\) west of south.
2.	85 m in south-west.
3.	25 m at \(\tan^{-1}(\frac{3}{4})\) west of south.
4.	15 m at \(\tan^{-1}(\frac{3}{4})\) west of south

 

An aircraft is flying horizontally at a height of 1 km from the ground with a speed of 200 m/s. An anti-craft missile launcher kept at a point on the ground which is in the vertical plane of the motion of aircraft. The muzzle velocity of the missile is 600 m/s. The missile is fired at a time when the aircraft was vertically above the anti-craft missile launcher. At what angle with horizontal should it be fired so as to hit the aircraft?

(1) ${\sin }^{-1}\left(\frac{2}{6}\right)$

(2) ${\cos }^{-1}\left(\frac{1}{3}\right)$

(3) ${\tan }^{-1}\left(3\right)$

(4) Just vertically upward

A man can throw a stone to a maximum height 'h'. The greatest horizontal distance up to which he can throw the stone is

(1) h

(2) 2h

(3) $\frac{\mathrm{h}}{2}$

(4) 4h

An oblique projectile is projected with a speed u. It takes time t, to reach the maximum height and time t, to come back to the ground. Air resistance is not neglected, then $\frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}$ is

(1) > 1

(2) < 1

(3) = 1

(4) Depends on the angle of projection

The speed of a projectile projected from level ground at its maximum height is found to be half of its speed of projection (u). Its maximum height is:

1.  $\frac{3{\mathrm{u}}^2}{8\mathrm{g}}$

2.  $\frac{3{\mathrm{u}}^2}{2\mathrm{g}}$

3.  $\frac{\sqrt{3}{\mathrm{u}}^2}{2\mathrm{g}}$

4.  $\frac{3{\mathrm{u}}^2}{4\mathrm{g}}$

A body moved along x-axis and y-axis according to the equation,

$x=2\sin \theta$
$y=3\cos \theta$

What is the trajectory followed by the body?

1.  

2.  

3.  

4.  

A particle of mass \(m\) is projected with a velocity at an angle with the horizontal into a uniform gravitational field. The slope of the trajectory varies with horizontal distance \(x\) as:

1.		2.
3.		4.

A projectile thrown at an angle 30° with horizontal from the level ground reaches a maximum height of 20 m. What will be the maximum height if it is thrown at an angle 60° with the same speed?

(1) 20 m

(2) 30 m

(3) 50 m

(4) 60 m

A body moving in a uniform circular motion with speed v. The magnitude of the change in its velocity after it rotates by an angle 120° is:
1. \(2v\)
2. \(\sqrt{3}v\)
3. \(v\)
4. \(\frac{\sqrt{3}}{2}v\)

A car moves on a circular path such that its speed is given by v = Kt, where K =constant and t is time. Also given: radius of the circular path is r. The net acceleration of the car at time t will be:

1. $\sqrt{{\mathrm{K}}^2 + {\left(\frac{{\mathrm{K}}^2{\mathrm{t}}^2}{\mathrm{r}}\right)}^2}$

2. 2K

3. K

4. $\sqrt{{\mathrm{K}}^2 + {\mathrm{K}}^2{\mathrm{t}}^2}$