A fighter plane flying horizontally at an altitude of \(1.5~\text{km}\) with a speed of \(720~\text{km/hr}\) passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed $\mathrm{}$\(600~\text{m/s}\) to hit the plane?

1.	At an angle of \(\sin^{ - 1}(1/3)\) with the vertical.
2.	Atanangleof\(\cos^{ - 1}(1/3)\)withthevertical.
3.	Atanangleof\(\tan^{ - 1}(1/3)\)withthevertical.
4.	Atanangleof\(\cot^{ - 1}(1/3)\)withthevertical.

 

A cyclist is riding at a speed of 27 km/h. As he approaches a circular turn on the road of a radius of 80 m, he applies brakes and reduces his speed at a constant rate of 0.50 m/s every second. What is the magnitude of the initial acceleration of the cyclist on the circular turn?

1. 0.66 ${\mathrm{ms}}^{-2}$

2. 0.56 ${\mathrm{ms}}^{-2}$

3. 0.86 ${\mathrm{ms}}^{-2}$

4. 0.16 ${\mathrm{ms}}^{-2}$

For a projectile, the angle between the velocity and the x-axis as a function of time is given by:

$\left(1\right)<mspace\; width="1em"></mspace>\mathrm{\theta }\left(\mathrm{t}\right)={\cos }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}-\mathrm{gt}}{{\mathrm{u}}_{\mathrm{x}}}\right)$

$\left(2\right)<mspace\; width="1em"></mspace>\mathrm{\theta }\left(\mathrm{t}\right)={\sin }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}-\mathrm{gt}}{{\mathrm{u}}_{\mathrm{x}}}\right)$

$\left(3\right)<mspace\; width="1em"></mspace>\mathrm{\theta }\left(\mathrm{t}\right)={\cot }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}-\mathrm{gt}}{{\mathrm{u}}_{\mathrm{x}}}\right)$

$\left(4\right)<mspace\; width="1em"></mspace>\mathrm{\theta }\left(\mathrm{t}\right)={\tan }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}-\mathrm{gt}}{{\mathrm{u}}_{\mathrm{x}}}\right)$

A truck starts from rest and accelerates uniformly at \(2.0~\text{ms}^{-2}\). At \(t = 10~\text{s}\), a stone is dropped by a person standing on the top of the truck (\(6\) m high from the ground). What is the acceleration of the stone at \(t = 11~\text{s}\)? (Neglect air resistance.)
1. \(10\) ms^–2 (upward)
2. \(15\) ms^–2 (downward)
3. \(10\) ms^–2 (downward)
4. \(15\) ms^–2 (upward)

A particle is moving along a circle such that it completes one revolution in \(40\) seconds. In \(2\) minutes \(20\) seconds, the ratio of \(|displacement| \over distance\) will be:
1. \(0\)
2. \(\frac{1}{7}\)
3. \(\frac{2}{7}\)
4. \(\frac{1}{11}\)

Consider the motion of the tip of the second hand of a clock. In one minute (assuming \(R\) to be the length of the second hand), its:

A car moves with a speed of \(60\) km/h for \(1\) hour in the east direction and with the same speed for \(30\) min in the south direction. The displacement of the car from the initial position is:

At any instant, the velocity and acceleration of a particle moving along a straight line are v and a. The speed of the particle is increasing if

(1) v>0, a>0

(2) v<0, a>0

(3) v>0, a<0

(4) v>0, a=0

If v is the velocity of a body moving along x-axis, then acceleration of body is

(1) $\frac{dv}{dx}$

(2) $v\frac{dv}{dx}$

(3) $x\frac{du}{dx}$

(4) $v\frac{dx}{dv}$

If a body is moving with constant speed, then its acceleration

(1) Must be zero

(2) May be variable

(3) May be uniform

(4) Both (2) & (3)