$A$ $1.5 \,kg$ ball is shot upward at an angle of $34^{\circ}$ to the horizontal with an initial speed of $20 \,m/s$. The maximum height reached by the ball is (use $\cos 34^{\circ} = 0.83$ and $\sin 34^{\circ} = 0.56$): (in $\,m$)

$A$ ball is rolled off the edge of a horizontal table at a speed of $4\, m/s$. It hits the ground after $0.4\, s$. Which statement given below is true?

$A$ ball thrown by one player reaches the other in $2 \ s$. The maximum height attained by the ball above the point of projection will be about ....... $m$. (Take $g = 10 \ m/s^2$)

$A$ bob of mass $0.1\; kg$ hung from the ceiling of a room by a string $2\; m$ long is set into oscillation. The speed of the bob at its mean position is $1\; m s^{-1}$. What is the trajectory of the bob if the string is cut when the bob is
$(a)$ at one of its extreme positions,
$(b)$ at its mean position.

Two projectiles are projected with the same initial velocities at $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their ranges is $1 : x$. The value of $x$ is:

Three identical balls are projected with the same speed at angles $30^{\circ}$,$45^{\circ}$,and $60^{\circ}$. Their ranges are $R_1$,$R_2$,and $R_3$ respectively. Then: