A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected with the same speed at an angle of $30^o$ with the horizontal. At the highest point, the ratio of their potential energies is

A body is projected at an angle $\theta $ with horizontal, another body is projected with the same speed at an angle $\theta $ with the vertical then the ratio of the maximum height is

The initial velocity of a particle of mass $2\,kg$ is $(4 \hat{ i }+4 \hat{ j })\,m / s$. A constant force of $-20 \hat{ j }\,N$ is applied on the particle. Initially, the particle was at $(0,0)$. Find the $x$-coordinate of the point where its $y$-coordinate is again zero.$..........\,m$

A cricketer can throw a ball to a maximum horizontal distance of $100 \,m$. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is  ......... $m$

A projectile is projected from ground with initial velocity $\vec u\, = \,{u_0}\hat i\, + \,{v_0}\hat j\,$. If acceleration due to gravity $(g)$  is along the negative $y-$ direction then find maximum displacement in $x-$ direction

Two projectile thrown at $30^{\circ}$ and $45^{\circ}$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is