If $x$ and $y$ coordinates of a projectile as a function of time are given as $24t$ and $43.6t - 4.9t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2 \text{ s}$ is . . . . . . .

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The velocity of projection is........ $ms^{-1}$.

The horizontal range is four times the maximum height attained by a projectile. The angle of projection is .......... $^o$

$A$ cart is moving horizontally along a straight line with a constant speed of $30\,m/s$. $A$ projectile is to be fired from the moving cart in such a way that it will return to the cart (at the same point on the cart) after the cart has moved $80\,m$. At what velocity (relative to the cart) must the projectile be fired? (Take $g = 10\,m/s^2$)

The maximum horizontal range of a projectile is $400\;m$. What is the maximum height attained by it (in $;m$)?

$A$ small object is thrown at an angle $45^{\circ}$ to the horizontal with an initial velocity $v_0$. The velocity is averaged for the first $\sqrt{2} \,s$ and the magnitude of the average velocity comes out to be the same as that of the initial velocity, i.e.,$|v_0|$. The magnitude $|v_0|$ will be (take $g=10 \,m/s^2$):