When a projectile is launched from a height of h\displaystyle {h} with an initial velocity of v0\displaystyle {v}_{{0}} and an initial trajectory at an angle of θ\displaystyle \theta with the positive x\displaystyle {x} axis, the path of the projectile is given by x(t)=(v0cos⁡θ)t\displaystyle {x}{\left({t}\right)}={\left({v}_{{0}}{\cos{\theta}}\right)}{t} and y(t)=h+(v0sin⁡θ)t−16t2\displaystyle {y}{\left({t}\right)}={h}+{\left({v}_{{0}}{\sin{\theta}}\right)}{t}-{16}{t}^{{2}}. Eliminate the parameter t\displaystyle {t} from these parametric equations to derive the general rectangular equation for the path of the projectile. Use your result to determine h\displaystyle {h}, θ\displaystyle \theta, and v0\displaystyle {v}_{{0}} for the projectile whose motion is described by y=−.005x2+x+5\displaystyle {y}=-{.005}{x}^{{2}}+{x}+{5}. Assume distance is measured in feet and time is measured in seconds.

(a) Write the general rectangular equation derived from these parametric equations by eliminating the parameter. You may enter v_0 for v0\displaystyle {v}_{{0}}.

      y=\displaystyle {y}=   

(b) Assuming the general equation above models the motion of a projectile, identify the the initial height, the initial trajectory angle theta, and the initial velocity of a projectile whose motion is described by y=−.005x2+x+5\displaystyle {y}=-{.005}{x}^{{2}}+{x}+{5}.

     h=\displaystyle {h}= feet         

      θ=\displaystyle \theta= radians     

    v0=\displaystyle {v}_{{0}}= feet per second          

License