From 83f94fb96951f70f1cc9a322f17e18cc6ca4b11d Mon Sep 17 00:00:00 2001 From: Loic Guegan Date: Mon, 4 Oct 2021 17:53:12 +0200 Subject: Update project --- projects/projectile/index.html | 15 +++++++++++++-- 1 file changed, 13 insertions(+), 2 deletions(-) (limited to 'projects/projectile/index.html') diff --git a/projects/projectile/index.html b/projects/projectile/index.html index 455b6b6..d56edd3 100644 --- a/projects/projectile/index.html +++ b/projects/projectile/index.html @@ -15,7 +15,7 @@
-
\(v_0\)
+
\(v_{0,x},v_{0,y}\)
\(m.s\)
@@ -34,4 +34,15 @@


Projectile Motion

-\[ \int_{0}^{10} \frac{56}{875} \] +

To determine to position of the projectile we should compute the position vector \(\vec{r}=x(t)\vec{i}+y(t)\vec{i}\).

+
\(x(t)\):
+

We know from Newton second law that \(\sum \vec{F} = m\times \vec{a}_x = m\times a_x(t)\vec{i}\)

+

However, the projectile as a constant speed along \(\vec{i}\). Hence, \(a_x(t) = 0 \).

+

Thus:

+\[ x(t) = \int_{t_0}^t v_{0,x}dt = v_{0,x}t + C = v_{0,x}t + x_0\] +
\(y(t)\):
+

We know from Newton second law that \(\sum \vec{F} = m\times \vec{a}_y = m\times a_y(t)\vec{i}\)

+

The projectile is under the influence of the gravity that is oriented downwarde. Hence, \(a_y(t) = -g \).

+

Thus:

+\[ v_y(t) = \int_{t_0}^t a_{y}(t)dt = -gt+C = -gt + v_{0,y}\] +\[ y(t) = \int_{t_0}^t v_y(t)dt = -\frac{1}{2}gt^2 + v_{0,y}t+C=-\frac{1}{2}gt^2 + v_{0,y}t+y_0\] -- cgit v1.2.3