Blog Post 2; IRC

Here is our application; Charlie is launching his homemade rocket and recording the height of the rocket at each second. The data for this was taken from http://oerl.sri.com/instruments/cd/studassess/instr34/instr34.html How do we find the velocity of this rocket at 4 seconds?

An Excel graph and table I made can be seen down below, however I couldnt get excel to add secant or tangent lines so I had to graph this by hand and scan it. Looking at the scanned image you can see the three secant lines I've drawn. and a tangent line coming going trough the point X, which is (4, 67.2)  

So first the ARC of X, A is equal to 123.2 - 67.2 / 11 - 4  = 56/7 = 8 feet/second, the ARC of X, B is equal to  115.2 - 67.2 / 9 - 4 = 48/5 = 9.6 feet per second, the ARC of X, C is equal to 108.8 - 67.2 / 8 - 4 = 10.4 

Essentially what this means is that the rocket's speed is slowing down as it gets to the top of the parabola and as the point we are using for our secant line gets closer to our X value the ARC is going up. Thats because gravity is working against the initial velocity the rocket was fired with. Now that we've drawn our tangent line, passing through our X and through to a point Y (8, 120), we can find the IRC. 120 - 67.2 / 8 - 4 = 52.8/4 = 13.2 feet per second is our IRC at our point X. This essentially means that the speed or velocity at our X point is 13.2 feet/second. Because the values we were getting for the slope of our secant lines were getting larger as they got closer and closer to our x point we can see they were actually growing closer and closer to the slope of our tangent line that goes through our X point. Because the tangent line is linear, the slope is the same at all points therefore by finding the slope of the tangent line we found the slope at our point X which is also called the Instantaneous Rate of Change.