- #1

babaliaris

- 116

- 15

**two independent straight line motions**. But this can give you a way to calculate total velocities or accelerations, just by adding its individual component of each vector.

If the initial position of the projectile is

$$

r = (x_0, y_0)

$$

then

**(1)**

$$

v = v_xi + v_yj \\

a = a_xi + a_yj

$$

where

**(2)**

$$

v_x = \frac{dx}{dt}, v_y = \frac{dy}{dt} \\

a_x = \frac{v_x}{dt}, a_y = \frac{v_y}{dt}

$$

SO

**(3)**

$$

v_x = v_0, v_y = a*t \\

x-x_0 = v_0t, y-y_0 = \frac{1}{2}at^2

$$

Using the equations in

**(3)**you can find the individual coefficients of the total

**v**and

**a**in

**(1)**independently (well a is just -g here but anyways). But if you know the Δx and Δy of the two motions can you somehow find the

**length of the path that the projectile travels without knowing the function of the path itself**?