Vertical projectile motion

Vertical projectile motion

change in time for vertical projectile motion

•  $y=v_it\sin\theta+\frac{1}{2}gt^2$  

• so

•  $\Delta t=\frac{2v_i\sin\theta}{\left(-g\right)}$  

horizontal (x) displacement

•  $x=v_{i_{ }}t\cos\theta$  

• so

•  $\Delta x=\frac{v_i^2\sin\left(2\theta\right)}{\left(-g\right)}$  

maximum height

•  $v_y=v_i\sin\theta+gt$  

•  $v_y=0$  at max height

•  $t_{vy}=\frac{\Delta t}{2}$  

•  $t_{vy}=\frac{v_i\sin\theta}{\left(-g\right)}$  sub into DE

•  $h_{\max}=\frac{v_i^2\sin^2\theta}{\left(-g\right)}+\frac{\frac{1}{2}g\left(v_i^2\sin^2\theta\right)}{g^2}$  

•  $h_{\max}=\frac{v_i^2\sin^2\theta}{2\left(-g\right)}$