Mathematica Project - Position, Velocity and Acceleration

A rocket is fired vertically upward into the air from a launching platform 100 ft above the ground. The platform is then retracted, and the rocket is allowed to fall to the ground.

The height (in ft) of the rocket relative to the ground t seconds after launch is given by:

s(t)=-16t^2+80t+100

1) Using Mathematica, define a function s(t).

2) Find the average velocity for t=1 ∈[1,2].

3) Find the velocity function, v(t). You'll want to define this as a function in Mathematica as well, so that you can refer to it easily later.

4) Find the instantaneous velocity at t=2s. How does this velocity compare with the average velocity you found in problem 2? Explain.

5) Find the equation of the line tangent to (s)t at t=2, and plot both this line and s(t) on one set of coordinate axes. Is your line actually tangent to the curve? Does the slope look right?

6) When does the rocket reach its highest point, and what is the velocity then?

7) Use Mathematica's NSolve command to find out when the rocket lands. What is its velocity when it hits the ground?

8) Plot s(t) and v(t) together on one set of coordinate axes. What do you notice about v(t) when s(t) is increasing? What about when s(t) is decreasing? At its maximum?

9) Find the acceleration function, a(t). What are the units for acceleration in this problem? Why is a(t) always negative, and what does it tell you about the velocity in this problem?

10) Notice that, on the way up, the rocket's velocity is positive, and its acceleration is negative. Is the rocket speeding up or slowing down? On the way down, both the velocity and acceleration are negative. Is the rocket speeding up or slowing down then?