# Range and height of a projectile

#### Question P2.7.5

The range of a projectile launched at an angle $\alpha$ and speed $v$ on flat terrain is: $$R = \frac{v^2\sin2\alpha}{g},$$ where $g$ is the acceleration due to gravity which may be taken to be $9.81\;\mathrm{m\,s^{-2}}$ for Earth. The maximum height attained by the projectile is given by: $$H = \frac{v^2\sin^2\alpha}{2g}.$$ (We neglect air resistance and the curvature and rotation of the Earth.) Write a function to calculate and return the range and maximum height of a projectile, taking $\alpha$ and $v$ as arguments. Test it with the values $v = 10\;\mathrm{m\,s^{-1}}$ and $\alpha = 30^\circ$.

#### Solution

To access solutions, please obtain an access code from Cambridge University Press at the Lecturer Resources page for my book (registration required) and then sign up to scipython.com providing this code.