a simple Model (model 1)of distance,d meters,fallen in time t seconds by free-fall skydiver is d(t)=4.9t^2
a. sketch the model
b. a different model (model 2) for the distance travelled by a skydiver is d(t)=4.9t^2-0.1t^2.sketch a graph of this function
I think your second model has a typo. Why not just say d(t) = 4.8t^2 ?
At any rate, you can plot multiple curves on the same axes here
http://www.wolframalpha.com/input/?i=plot+y%3D4.9t%5E2%2C+y%3D4.8t%5E2
If the second equation has to be tweaked, adjust it and fix the graphs.
To sketch the models, follow these steps:
a. Sketching Model 1 (d(t) = 4.9t^2):
1. Choose suitable values for t, such as 0, 1, 2, and so on.
2. Plug these values into the equation d(t) = 4.9t^2 to calculate the corresponding distances.
3. Plot the ordered pairs (t, d) on a coordinate plane.
4. Connect the plotted points to form a smooth curve.
b. Sketching Model 2 (d(t) = 4.9t^2 - 0.1t^2):
1. Repeat steps 1 and 2 from above to calculate the distances for different values of t.
2. Plot the ordered pairs (t, d) on the same coordinate plane used for Model 1.
3. Connect the plotted points to form a smooth curve.
Note: Since the equations are quadratic, the shape of the graph will be a downward-opening parabola. The main difference between the two models is that Model 2 subtracts an additional term (-0.1t^2), which will cause the graph to be slightly lower compared to Model 1.
Remember to label the axes with appropriate units (time in seconds and distance in meters) and add a clear title indicating the model being represented.