Neglecting air resistance,the time of flight of a projectile is determined by:

$A$ stone is thrown vertically at a speed of $30 \,ms^{-1}$ making an angle of $45^{\circ}$ with the horizontal. What is the maximum height reached by the stone (in $\,m$)? Take $g=10 \,ms^{-2}$.

$A$ 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 $g = 10\,m/s^2$)

$A$ cricketer can throw a ball to a maximum horizontal distance of $100 \; m$. How much high above (in $m$) the ground can the cricketer throw the same ball?

Two seconds after projection,a projectile is travelling in a direction inclined at $30^o$ to the horizontal. After one more second,it is travelling horizontally. What is the magnitude and direction of its velocity at the initial point?

$A$ body is projected from the ground with a velocity $v = (3 \hat{i} + 10 \hat{j}) \text{ m/s}$. The maximum height attained and the range of the body respectively are (given $g = 10 \text{ m/s}^2$):