A cricketer can throw a ball to a maximum horizontal distance of \(100~\text{m}\). How much high above the ground, can the cricketer throw the same ball?
1. \(50~\text{m}\)
2. \(60~\text{m}\)
3. \(75~\text{m}\)
4. \(100~\text{m}\)

The ceiling of a long hall is \(25~\text m\) high. What is the maximum horizontal distance that a ball thrown with a speed of \(40~\text{m/s}\) can go without hitting the ceiling of the hall?
1. \(150.5~\text m\)
2. \(165.6~\text m\)
3. \(145.3~\text m\)
4. \(158.2~\text m\)

A bullet fired at an angle of 30° with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away? Assume the muzzle speed to be fixed, and neglect air resistance.

1. Yes
2. No
3. Depends on the mass of the bullet
4. None of the above

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?

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)