Q 1 :    

The angle of projection for a projectile to have same horizontal range and maximum height is                       [2024]

• ${\tan }^{-1}\left(2\right)$

   

• ${\tan }^{-1}\left(\frac{1}{2}\right)$

   

• ${\tan }^{-1}\left(4\right)$

   

• ${\tan }^{-1}\left(\frac{1}{4}\right)$

   

Q 2 :    

A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to 4R. The angle of projection $\theta$ is then given by                                [2024]

• ${\sin }^{-1}{\left[\frac{2g{T}^2}{{\pi }^{2}R}\right]}^{\frac{1}{2}}$

   

• ${\sin }^{-1}{\left[\frac{{\pi }^{2}R}{2g{T}^2}\right]}^{\frac{1}{2}}$

   

• ${\cos }^{-1}{\left[\frac{2g{T}^2}{{\pi }^{2}R}\right]}^{\frac{1}{2}}$

   

• ${\cos }^{-1}{\left[\frac{\pi R}{2g{T}^2}\right]}^{\frac{1}{2}}$

   

Q 3 :    

The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is _____ m.          [2024]

Q 4 :    

A body of mass M thrown horizontally with velocity $v$ from the top of the tower of height H touches the ground at 100 m from the foot of the tower. A body of mass 2M thrown at a velocity $\frac{v}{2}$from the top of the tower of height 4H will touch the ground at a distance of _____ m.            [2024]