A dart is thrown upwards with an initial velocity of 64 ft./s at an angle of elevation of 52° consider the position T with no air resistance, find the parametric equation that models a solution as well as find all possible values of X that represent the solution

Solution Using the equation of motion and finding the horizontal displacement $$u=64c0s\left(52\right)$$ a=0 $$x\left(t\right)=64c0s\left(52\right)t+\frac{1}{2}\left(0\right)t^2$$ $$x\left(t\right)=64c0s\left(52\right)t$$ Since acceleration due to gravity acts on the dart in a vertically downward direction a=-32 ft/s u=64sin(52) $$y\left(t\right)=64sin\left(52\right)t+\frac{1}{2}\left(-32\right)t^2$$ $$y\left(t\right)=64sin\left(52\right)t-16t^2$$