$A$ body of mass $1 \, kg$ is projected from the ground at an angle of $30^{\circ}$ with the horizontal on level ground at a speed of $50 \, m/s$. The magnitude of the change in momentum of the body during its entire flight is ....... $kg \cdot m/s$ $(g = 10 \, m/s^2)$.

Which one of the following statements is not true about the motion of a projectile?

$A$ body is projected into a vertical $X-Y$ plane with the $X$-axis along the horizontal and the $Y$-axis along the vertical with an initial velocity $(10 \hat{i} + p \hat{j}) \ m/s$. If the maximum height reached by the body is $50 \%$ of its range,then the value of $p$ is:

$A$ projectile is given an initial velocity of $(\hat{i} + 2\hat{j}) \, m/s$,where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g = 10 \, m/s^2$,the equation of its trajectory is:

It is possible to project a particle with a given velocity in two possible ways so as to make them pass through a point $P$ at a horizontal distance $r$ from the point of projection. If $t_1$ and $t_2$ are times taken to reach this point in two possible ways, then the product $t_1 t_2$ is proportional to

If the instantaneous velocity of a particle projected as shown in the figure is given by $v = a \hat{i} + (b - ct) \hat{j}$,where $a, b$,and $c$ are positive constants,the range on the horizontal plane will be