Question

How to find the equation of trajectory using conservation of energy theorem

Answer 1

$E_p+Ek = const$

$E_p,E_k-\text{potential and kinetic energy of the body}$

$E_p = mgh$

$Ек = \frac{mV^2}{2}$

$\text{let }E_k =0;E_p=mgh_{max};const= mgh_{max}$

$mgh +\frac{mV^2}{2}=mgh_{max}$

$h= h_{max}-\frac{V^2}{2g}$

$h(t)= h_{max}-\frac{V(t)^2}{2g};V(t) -\text{change in speed over time}$

Answer:$h(t)=h_{max}-\frac{V^2(t)}{2g};V(t)-\text{changein speed over time}$