Provide an appropriate response.Derive the equations x = x0 + (v0 cos ?)t, y = y0 + (v0 sin ?)t - gt2by solving the following initial value problem for a vector r in the plane. Differential equation: = -gj Initial conditions: r(0) = x0i + y0j (0) = v0 cos ?)i + (v0 sin ?)j

Question

What will be an ideal response?

Answer 1

x-coordinate:
  = 0, so  = constant = v_0,x = v₀c os ?
 Then, x =  dt = dt = v₀ cos ? t + x₀

y-coordinate:
  = -g , so  =  dt =  dt = -gt + v_y,0 = v₀ sin ? - gt 
 y = dt = dt = v₀ sin ? t - gt² + y₀