Motion in a Plane — Physics STD 11 Science — Question

1. Horizontal range: It is the horizontal distance covered by the body between its point of projection and the point of hitting the ground, when both points are on same horizontal plane. It is denoted by R.

$\therefore\ \text{R}=\text{u}\cos\theta_0\times$ Total time of flight (T)

$=\text{u}\cos\theta_0\times\frac{2\text{u}\sin\theta_0}{\text{g}}$

$=\frac{\text{u}^2}{\text{g}}2\sin\theta_0\cos\theta_0$

$=\frac{\text{u}^2}{\text{g}}\sin2\theta_0$

$\text{R}=\frac{\text{u}^2\sin2\theta_0}{\text{g}}$

2. Maximum height: Maximum height (h_max) is the maximum vertical height attained by the body above the point of projection during its flight.

Here, AH is referred as the maximum height attained against gravity. At highest point vertical component of velocity become zero.

Using, v² = u² + 2as, we have

$0=\text{u}^2\sin^2\theta_0-2\text{gh}_\text{max}$

$\Rightarrow\ \text{h}_\text{max}=\frac{\text{u}^2\sin^2\theta_0}{2\text{g}}$