$A$ body is projected from the ground at an angle of $45^{\circ}$ with the horizontal. Its velocity after $2 \, s$ is $20 \, m/s$. The maximum height reached by the body during its motion is $m$. (use $g = 10 \, m/s^2$)

The angle of projection at which the horizontal range and maximum height of a projectile are equal is

The path of a projectile is given by the equation $y = ax - bx^2$,where $a$ and $b$ are constants,and $x$ and $y$ are the horizontal and vertical distances of the projectile from the point of projection,respectively. The maximum height attained by the projectile and the angle of projection are respectively:

$A$ projectile object is thrown in the upward direction making an angle of $60^{\circ}$ with the horizontal with velocity of $140 \ m/s$. Then,the time after which its velocity makes an angle $30^{\circ}$ with the horizontal is (Take,$g=10 \ m/s^2$)

$A$ missile is fired for maximum range at your town from a place $100 \, km$ away from you. If the missile is first detected at its half-way point,how much warning time will you have? (Take $g = 10 \, m/s^2$)

$A$ body of mass $m$ thrown up vertically with velocity $v_1$ reaches a maximum height $h_1$ in $t_1$ seconds. Another body of mass $2m$ is projected with a velocity $v_2$ at an angle $\theta$. The second body reaches a maximum height $h_2$ in time $t_2$ seconds. If $t_1 = 2t_2$,then the ratio $\left(\frac{h_1}{h_2}\right)$ is