Projectile motion equations

Question

starting with the projectile motion equations , show that the launch speed of the projectile is given by the following equation : v_i = sqrt (xf² *g) /(2y_i)

The square root is over the entire thing. 

 

I am guessing I need to substitute something but am not sure what. 

Answer 1

assumming angle=0  (launch horizontally)

X_f=V_i*t

=> V_i=X_f/t

 

t=sqrt(2y_i/g)

 

=> V_i=X_f/sqrt(2yi/g)=sqrt(X_f²*g)/2y_i