Physics > Motion in Two Dimension > 3.0 Ground to ground projectile motion
Motion in Two Dimension
1.0 Introduction
2.0 Projectile motion
3.0 Ground to ground projectile motion
3.1 Maximum height
3.2 Time of flight
3.3 Range
3.4 Trajectory of a projectile
3.5 Summary
3.6 Solved Examples
4.0 Projectile thrown parallel to the horizontal
5.0 Projectile on an inclined plane
6.0 Relative motion between two projectiles
3.1 Maximum height
3.2 Time of flight
3.3 Range
3.4 Trajectory of a projectile
3.5 Summary
3.6 Solved Examples
At maximum height, the vertical velocity is zero. So,
${\overrightarrow u _y} = u\sin \theta $
${\overrightarrow a _y}=-g$
${\overrightarrow v _y}=0$
${\overrightarrow s _{y}}=+H_{Max}$
Therefore we can write kinematics equation which relates displacement and velocity as,
$$v_y^2 = u_y^2 + 2{{\vec a}_y}.{{\vec s}_y}$$$$0 = {u^2}{\sin ^2}\theta + 2\left( { - g} \right)\left( { + {H_{\max }}} \right)$$$${H_{\max }} = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}$$
