Hi

I have spent ages trying to work out the way to program my TI-83 calculator to solve the following... I would appreciate guidance or direction to a site that can show me how to solve the following;-

motion of two stage rocket is stated by it height y in metres above the ground since t seconds since launch.

Flies vertically Ist stage burns for 5 seconds and cuts out. 2nd stage rocket is under gravity alone.

modelled by the equations

Stage 1 height y = 10t2

time 0¡Ü t <5

stage 2 height y = -5t2 + 150t - 375

time t >5

Question asks you plot function on ti 83, using an appropriate window for time(s)
hence sketch a position time graph for each stage of flight ading labels etc..

also ask you to plot use the n deriv function to plot rate of change of function.

If I can find the basic means of plotting graph I should be able to answer the question but cannot find anything in manual that is similar to solving a question of this type.

I appreciate yout time and effort and thanks !!!!!!!!

To plot the function on your TI-83 calculator and sketch the position-time graph for each stage of flight, you can follow these steps:

1. Turn on your TI-83 calculator and go to the graphing mode by pressing the "Y=" button.

2. Enter the equation for the first stage height, y = 10t^2, where t is the time in seconds and ^ denotes exponentiation. Press the "ENTER" key to confirm the equation.

3. For the time range 0 ≤ t < 5, you need to set the window appropriately. Press the "WINDOW" button on your calculator.

4. Adjust the Xmin and Xmax values to cover the time range. In this case, set Xmin = 0 and Xmax = 5.

5. Set the Ymin and Ymax values to cover the height range. Since the equation is y = 10t^2, the height will increase with increasing time. So you can choose a suitable Ymin and Ymax values, such as Ymin = 0 and Ymax = 500.

6. Press the "GRAPH" button to plot the graph. You should see the position-time graph for the first stage.

7. To plot the graph for the second stage, enter the equation y = -5t^2 + 150t - 375, where t > 5. Press the "ENTER" key to confirm the equation.

8. Adjust the Xmin and Xmax values to cover the time range for the second stage. Since t > 5, you can set Xmin = 5 and choose a suitable Xmax value based on the total flight duration.

9. Set the Ymin and Ymax values to cover the height range for the second stage. Similar to the previous step, choose suitable values for Ymin and Ymax.

10. Press the "GRAPH" button again to plot the graph. You should see the position-time graph for the second stage.

To plot the rate of change (derivative) of the function, you can use the "nDeriv" function on your TI-83 calculator. Follow these steps:

1. Press the "Y=" button and enter the equation for the function you want to find the derivative of.

2. Go to the "GRAPH" menu by pressing the "2nd" and "GRAPH" buttons simultaneously.

3. Select the "nDeriv(" option by pressing the corresponding number or using the arrow keys and then pressing "ENTER".

4. Enter the equation of the function you want to differentiate, and then enter the variable (t in this case) and the value of t at which you want to find the derivative.

5. Press "ENTER" to calculate the derivative value.

6. To plot the graph of the derivative, repeat steps 3-5 for a range of t values and plot the points on the graph.

I hope this helps you plot the function and its derivative on your TI-83 calculator. If you have any further questions, feel free to ask.