- #1
babaliaris
- 116
- 15
So I just learned about projectile motion. I understand why you can study it as 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?
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?