A particle is projected in air at some angle to the horizontal, moves along parabola as shown in figure where $x$ and $y$ indicate horizontal and vertical directions respectively. Shown in the diagram, direction of velocity and acceleration at points $A, \,B$ and $C$.
$v_{x}=\text { Horizontal component of velocity }=v \cos \theta=\text { constant }$
$v_{y}=\text { Vertical component of velocity }=v \sin \theta$
Velocity will always be tangential to the curve in the direction of motion and acceleration is always vertically downward and is equal to $\mathrm{g}$.
Galileo writes that for angles of projection of a projectile at angles $(45 + \theta )$ and $(45 - \theta )$, the horizontal ranges described by the projectile are in the ratio of (if $\theta \le 45)$
Two projectiles are fired from the same point with the same speed at angles of projection $60^o$ and $30^o$ respectively. Which one of the following is true?
A boy playing on the roof of a $10\, m$ high building throws a ball with a speed of $10\, m/s$ at an angle $30^o$ with the horizontal. ........ $m$ far from the throwing point will the ball be at the height of $10\, m$ from the ground . $(g \,= \,10 m/s^2, \,sin \,30^o \,= \,\frac{1}{2}$, $\cos \,{30^o}\, = \,\frac{{\sqrt 3 }}{2}$)
A ball is projected from ground with a velocity $V$ at an angle $\theta$ to the vertical. On its path it makes an elastic collison with a vertical wall and returns to ground. The total time of flight of the ball is
A boy throws a ball in air at $60^o$ to the horizontal, along a road with a speed of $10\,ms^{-1}$ $(36\, km/h)$. Another boy sitting in a passing by car observes the ball. Sketch the motion of the ball as observed by the boy in the car, if car has a speed of $(18\, km/h)$. Give explanation to support your diagram.