# Engineering Class 12 – Escape Velocity, Kinematics, Integration

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In this class we expanded on our last class where we dropped a baseball from the second story. In this class we timed the fall and calculated the height of the drop.

• We measured a 1 second drop that yielded a 5m height.
• In todays class we used Kinematics to calculate the velocity, that the ball would hit the floor.
• We then discussed that we could do the same for the escape velocity of the Earth, EXCEPT, that gravity changes as we move away from the earth.
• We then used calculus to calculate the total energy at infinity distance away from the Earth!
• We did this by visualizing that we could perform successive additions of slices where the gravity was changing by a factor of (r/s)2.

$PE = \sum m*g_1*h_1 + m*g_2*h_2 + m*g_3*h_3 + m*g_n*h_n$

$\sum_{r}^{Infinity} g m \left (\frac{r}{s}\right )^2 \Delta s$

This concept of successive additions is the concept of Integration that we learned in the last couple of classes.

We then used Mathematica to perform the same Integration.

Here are the class notes:

-Edward