Question

Darivation
V=√u^(2)+g^(2)t^(2)-2ugt sin(θ)

Answer 1

$$v=\sqrt{v_x^2+v_y^2}$$

For projectile:

$$v=\sqrt{(u\cos{\theta})^2+(u\sin{\theta}-gt)^2}$$

$$v=\sqrt{u^2((\cos{\theta})^2+(\sin{\theta})^2)+(gt)^2-2ugt \sin(θ)}$$

$$v=\sqrt{u^2+g^2t^2-2ugt \sin(θ)}$$