The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $h_m$. Here $h_m$ as a function of $\phi$ can be represented as:

Two particles are projected from a tower in opposite directions horizontally with speed $10\,m/s$ each. At $t=1\,s$,match the following two columns.

Column $I$	Column $II$
$(A)$ Relative acceleration between two	$(p)$ $0$ $SI$ unit
$(B)$ Relative velocity between two	$(q)$ $5$ $SI$ unit
$(C)$ Horizontal distance between two	$(r)$ $10$ $SI$ unit
$(D)$ Vertical distance between two	$(s)$ $20$ $SI$ unit

$A$ particle is in uniform circular motion. Related to one complete revolution of the particle, which among the statements is incorrect?

$A$ projectile is launched at an angle $\alpha$ with the horizontal with a velocity $20 \; m/s$. After $10 \; s$,its inclination with the horizontal is $\beta$. The value of $\tan \beta$ will be: $(g = 10 \; m/s^2)$

The initial position of an object at rest is given by $3 \hat{i}-8 \hat{j}$. It moves with constant acceleration and reaches the position $2 \hat{i}+4 \hat{j}$ after $4 \, s$. What is its acceleration?

$A$ projectile is thrown with some initial velocity at an angle $\alpha$ to the horizontal. Its velocity when it is at the highest point is $(2/5)^{1/2}$ times the velocity when it is at height half of the maximum height. Find the angle of projection $\alpha$ with the horizontal. (in $^{\circ}$)